Вместо этого используйте ListBoxFor
:
@Html.ListBoxFor(m => m.Movies, new SelectList(Model.Movies, "id", "name"), "Select Movie", new { @class = "form-control"})
Или добавьте атрибут multiple
к DropDownListFor
@Html.DropDownListFor(m => m.Movies, new MultiSelectList(Model.Movies, "id", "name"), "Select Movie", new {multiple = "true", @class = "form-control"})