Try this
<asp:DropDownList ID="Inventory_No_dropdown"
runat="server"
Font-Bold="true"
onmousedown="this.size=5;"
onfocusout="this.size=1;"
ondblclick="this.size=1;"
class=""
CssClass="span3 dropmenuScroll" //or CssClass="dropmenuScroll"
Style="position: absolute !important;"
AppendDataBoundItems="True"
AutoPostBack="True"
onselectedindexchanged="Inventory_No_dropdown_SelectedIndexChanged">
<asp:ListItem Value="0" >--------SELECT--------</asp:ListItem>
</asp:DropDownList>
css style
.dropmenuScroll
{
height: 300px;
max-height: 300px;
overflow-y: scroll;
position:absolute;
}