With that chipset, your mobo is a socket 775, the CPU you're asking about is a newer ivy bridge which needs a socket 1155 (much newer) mobo. you could put a core 2 duo e4xxx series in there and be good to go.
i have core 2 duo e4400 right now but i want to play latest games so i am planning to buy radeon hd7770 1gb ddr5,corsair 450w smps,intel pentium g2020,and 4gb ram and after buying all this i cannot afford new mobo till 5-6 months so plz tell me any solution?
With a 7770, i'd just leave your CPU as is, you'll end up with a decent entry level gaming rig. If you sprung for an i5 and then threw in a 7770, you'd not see tons better performance with a lower-end GPU.