我也遇到这样的问题 但觉得代码没问题

亲，根据你的代码进行测试，代码是没有问题，项目部署之后，访问success.jsp，可直接跳转到Login.jsp.你看再试试

百度一下，你就知道

<?xml version="1.0" encoding="UTF-8"?>
<web-app version="3.0"
    xmlns="http://java.sun.com/xml/ns/javaee"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd">
  <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>first</servlet-name>
    <servlet-class>com.imcoo.first</servlet-class>
  </servlet>
  <servlet-mapping>
    <servlet-name>first</servlet-name>
    <url-pattern>/servlet/first</url-pattern>
  </servlet-mapping>
    <filter>
        <filter-name>firstfilter</filter-name>
        <filter-class>com.imcoo.firstfilter</filter-class>
        <init-param>
            <param-name>noLoginPath</param-name>
            <param-value>Login.jsp;fail.jsp;first</param-value>
        </init-param>
    </filter>
    <filter-mapping>
        <filter-name>firstfilter</filter-name>
        <url-pattern>/*</url-pattern>
    </filter-mapping>

</web-app>

package com.imcoo;

import java.io.IOException;
import java.util.Enumeration;

import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpSession;

public class firstfilter implements Filter {
    private FilterConfig config;
 @Override
 public void destroy() {
  // TODO Auto-generated method stub

 }

 @Override
 public void doFilter(ServletRequest arg0, ServletResponse arg1,
   FilterChain arg2) throws IOException, ServletException {
      HttpServletRequest request=(HttpServletRequest) arg0;
      HttpServletResponse response=(HttpServletResponse) arg1;
      HttpSession session=request.getSession();
      String noLoginPath=config.getInitParameter("noLoginPath");
      if(noLoginPath!=null){
       String[] array=noLoginPath.split(";");
       for(int i=0;i<array.length;i++){
        if(array[i]==null||"".equals(array[i])) continue;
        if(request.getRequestURI().indexOf(array[i])!=-1){
         arg2.doFilter(arg0, arg1);
         return;
        }
        
       }
       
      }
      if(session.getAttribute("name")!=null){
       arg2.doFilter(arg0, arg1);
      }
    
      else{
       response.sendRedirect(request.getContextPath()+"/Login.jsp");
      }
      System.out.println(session.getAttribute("name"));
 }

 @Override
 public void init(FilterConfig arg0) throws ServletException {
  // TODO Auto-generated method stub
          config=arg0;
 }

}

package com.imcoo;

import java.io.IOException;
import java.util.Enumeration;

import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpSession;

public class firstfilter implements Filter {
    private FilterConfig config;
 @Override
 public void destroy() {
  // TODO Auto-generated method stub

 }

 @Override
 public void doFilter(ServletRequest arg0, ServletResponse arg1,
   FilterChain arg2) throws IOException, ServletException {
      HttpServletRequest request=(HttpServletRequest) arg0;
      HttpServletResponse response=(HttpServletResponse) arg1;
      HttpSession session=request.getSession();
      String noLoginPath=config.getInitParameter("noLoginPath");
      if(noLoginPath!=null){
       String[] array=noLoginPath.split(";");
       for(int i=0;i<array.length;i++){
        if(array[i]==null||"".equals(array[i])) continue;
        if(request.getRequestURI().indexOf(array[i])!=-1){
         arg2.doFilter(arg0, arg1);
         return;
        }
        
       }
       
      }
      if(session.getAttribute("name")!=null){
       arg2.doFilter(arg0, arg1);
      }
    
      else{
       response.sendRedirect(request.getContextPath()+"/Login.jsp");
      }
      System.out.println(session.getAttribute("name"));
 }

 @Override
 public void init(FilterConfig arg0) throws ServletException {
  // TODO Auto-generated method stub
          config=arg0;
 }

}

亲，把配置文件和过滤器的代码贴出来看看吧