You should provide correct parameter name in action link and there is no need to specify parameters here :)
@{
foreach (string str in ViewBag.ServerNames)
{
<ul>
<img src="../../Content/Images/my_computer.png" alt="Computer Name"/>
<li >@Html.ActionLink(str.ToString(),"Index","Customer",
new{conName= str.ToString()} , null)</li>
</ul>
}