But Cook will have a long way to go to dethrone Australia skipper Steve Smith from the top of the ICC Rankings.
2/8
It is also worth to mention England captain Joe Root stands on 2nd position.
3/8
Banking on his 243 runs in the first Test, Cook jumped six positions to reach 6th spot in ICC Test rankings. This is also his best ranking in last three years.
4/8
The left-arm batsman is now just 8 ratings behind Indian skipper Virat Kohli in the Test rankings.
5/8
England thrashed visitors West Indies by an innings and 209 runs in the first Test match at Edgbaston, taking 1-0 lead in the three-match Test series.
6/8
With Cook in fine form and India not playing Test cricket till October, the England batsman looks certain to leave Virat Kohli behind.
7/8
The 32-year-old has 798 points, while Kohli has 806 points and takes 5th Position.
8/8
Former skipper Alastair Cook score magnificent 243 to guide hosts to mammoth 514/8 in the first innings.