Kohli’s India are in action against New Zealand this week as they build towards the World Cup in England later this year.
Kohli has been in stunning form of late and was awarded all three ICC awards – the first player in history to do so.
He picked up the Sir Garfield Sobers Trophy for ICC Cricketer of the Year, the ICC Men’s Test Player of the Year and the ICC ODI Player of the Year.
And Shastri claims India are fortunate to have him.
“To carry that kind of pressure of captaincy and clean up all the individual ICC awards as well is phenomenal. We have had great players who struggled to handle pressure when they were captain,” he told Cricbuzz.
“Then we had some captains who didn’t know what number to bat at – when they are good enough to go at number three, but they chose to go at six or seven.
“But here is a guy who is as dominant as Sir Vivian Richards. The closest I have seen to the great man. Virat is in your face, he wants to dominate and has a work ethic like no one else.
“Whether it comes to discipline, training, sacrifice or self-denial, it is unbelievable. I think India is lucky to have a leader of that sort.
“He reminds me of Imran Khan in many ways – in the way he sets the example and sets the standards, and goes about defining it in his own way and leading from the front.
“Virat is special, absolutely special, for someone to get runs in dominant fashion in South Africa, in Australia and in England. England was icing on the cake.
“Here’s a guy who has got 140 runs in 10 innings (2014) and then gets 590 runs with two masters of bowling in James Anderson and Stuart Broad.
“You won’t get better than that with the Dukes ball. And to get those runs as captain in a team that is being beaten is phenomenal.”
But Shastri thinks he can get even better when it comes to captaining the India side.
He added: “As far as I am concerned, tactically, there is still room for plenty of improvement as captain.
‘He has gotten better and better, and better, and I thought in the Australian Test series, tactically he outsmarted Australia. I still see more room across formats for him to evolve.
“As a captain, Virat will evolve further.”