Is there any way to fill grouped objects background in Illustrator?
Below is example how i want it, right now i simply just put white square behind them.
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If you really don't want to create a second object for the background, you can use some Appearance Panel trickery to add one....
Contentsin the panel
Effect > Convert to Shape > Rectangle
Extra Heightto zero.
However, there's really little reason to not merely draw a box behind the lines to create a fill. Then merely group the lines and the box.
The way you have done it with a rectangle behind the group is the way to "fill" behind a "group"- this is done often- you could also group the rectangle with the lines so they could easily be moved around together.
Alternately, you could combine the rectangle and the group of lines into a compound path (Object>compound path>make) so it is all one "object"- the disadvantage to this is that you would have a border around the entire shape which would be whatever your stroke color is- your example did not have this