Edit in JSFiddle

$(document).ready(function(){
  jQuery.expr[':'].Contains = function(a,i,m){
      return (a.textContent || a.innerText || "").toUpperCase().indexOf(m[3].toUpperCase())>=0;
  };

  function filterList(header, list) {
    var form = $("<form>").attr({"class":"filterform","action":"#"}),
        input = $("<input>").attr({"class":"filterinput","type":"text"});
    $(form).append(input).appendTo(header);

    $(input)
      .change( function () {
        var filter = $(this).val();
        if(filter) {

          $matches = $(list).find('a:Contains(' + filter + ')').parent();
          $('li', list).not($matches).slideUp();
          $matches.slideDown();

        } else {
          $(list).find("li").slideDown();
        }
        return false;
      })
    .keyup( function () {
        $(this).change();
    });
  }

  $(function () {
    filterList($("#form"), $("#list"));
  });
}(jQuery));

<div id="wrap">
<div class="product-head">
  <h1>list search</h1>
    <div id="form"></div>
    <div class="clear"></div>
</div>
  <ul id="list">
        <li><a href="#/Apple/">Apple</a></li>
        <li><a href="#/Squash/">Acorn Squash</a></li>
        <li><a href="#/Broccoli/">Broccoli</a></li>
        <li><a href="#/Carrot/">Carrot</a></li>
        <li><a href="#/Celery/">Celery</a></li>
        <li><a href="#/Lettuce/">Lettuce</a></li>
        <li><a href="#/Mushroom/">Mushroom</a></li>
        <li><a href="#/Onion/">Onion</a></li>
        <li><a href="#/Potato/">Potato</a></li>
        <li><a href="#/Pumpkin/">Pumpkin</a></li>
        <li><a href="#/Radish/">Radish</a></li>
        <li><a href="#/Squash/">Squash</a></li>
        <li><a href="#/strawberry/">Strawberry</a></li>
        <li><a href="#/SugarSnaps/">Sugar Snaps</a></li>
        <li><a href="#/tomato/">Tomato</a></li>
    </ul>
</div>