//meSel is an object of <select>
mySel.innerHTML = "<option value='name'>name</option>";
Code above failed on IE and is OK on FireFox.
I suspect that your variable mySel is obtaining its reference to the <select> tag in a way that IE doesn't support. But it's impossible to tell from the single line you show. Post the rest of your code.
var mySel = document.getElementById('my-select');
See this page to change select content in the fly with the Option() constructor which supports four parameters, the later two optional :
new Option(text, value, defaultSelected, selected)
Internet Explorer doesn't allow innerHTML to be used to update parts of elements of the page - such as table, select and probably anything else where the element uses more than one tag. See 007Julien's suggestion for how to properly insert an option
You can also use the Native DOM:
var option = document.createElement("option");
option.value = "foo";