Edit in JSFiddle

$(document).ready(function() {
    $("#addBtn").click(function(){
        $("#list").append($('<li class="list-item"><div class="input-group"><input class="form-control"value="'+$("#list li").length+'"/><div class="input-group-btn"><button class="delbtn btn btn-danger">削除</button></div></div></li>'))
    });
    $(document).on("click", '.list-item', function(){
        $('#list li')[$(this).index()].remove();
    })
});

<button id="addBtn" class="btn btn-default">追加</button>
<ul id="list" class="list-unstyled"></ul>