<script src="https://cdn.staticfile.org/jquery/2.2.4/jquery.min.js"></script>

<form action="" method="" onsubmit="return loginBtn_click();">

  <h3>Log in</h3>

  <input type="text" name="user" placeholder="user" id="user">

  <input type="password" name="pass" placeholder="password" id="pass">

  <input type="checkbox" id="remember" checked><br/><br/>

  <input type="submit" id="sub">

</form>

$(document).ready(function(){

​

  var strName = localStorage.getItem('keyName');

  var strPass = localStorage.getItem('keyPass');

  if(strName){

    $('#user').val(strName);

  }if(strPass){

    $('#pass').val(strPass);

  }

​

});

​

function loginBtn_click(){

  var strName = $('#user').val();

  var strPass = $('#pass').val();

  localStorage.setItem('keyName',strName);

  if($('#remember').is(':checked')){

    localStorage.setItem('keyPass',strPass);

  }else{

    localStorage.removeItem('keyPass');

  }

}

form{

  width: 300px;

  padding: 10px 0px 20px 30px;

  height:auto;

  border-radius: 6px;

  border-left:8px solid #19a049;

  background:#eee;

  margin:100px auto;

}

#user,#pass{

  padding: 8px;

  outline: none;

  background: transparent;

  border:1px solid #999;

  margin-top: 5px;

}

#sub{

  padding: 6px;

  outline: none;

  border:none;

  background: #19a049;

  color:#fff;

  width: 150px;

  border-radius: 6px;

  cursor: pointer;

}