Sorting in gridview with up and down arrow using mvc4

For displaying grid of data refer - Displaying a Grid of Data in ASP.NET MVC [^]

and

for sorting refer Sorting a Grid of Data in ASP.NET MVC[^].

Hope they help you.

[Update] as per comments added by OP.

Take a look at the article - Grid - MvcContrib[^], , which is one grid implementation in MVC.
In the sorting section of that article, it says like below.

When the data has been sorted on a column, the grid will place additional CSS classes in the column headings. If the column is currently sorted in ascending order then the appropriate "th" tag will have a class of sort_asc. Likewise, if the column is sorted in descending order then the css class will be sort_desc. These classes can be used to add additional styling (for example, to add up/down arrows). Please look at the MvcContrib.Examples.UI project for a complete example.

So you can add up and down icons also.
Take a look at MvcContrib Grid Part 6 - Sorting[^] for more details.

Try to implement this.

[/Update]

[Updating again](as per OP's comment)
After so many research, I found one example project, where up and down icons are working on grid sort columns.

Please go through the article ASP.NET MVC Paging/Sorting/Filtering using the MVCContrib Grid and Pager[^]. You will find the demo application or sorce code at the end of the article or just click NorthwindSales_MvcContrib.zip[^] to download.

I have downloaded it and tested at my local. It works fine and the up down icons also coming on the sorted columns.
[/Updating again]

Thanks...