Cook was dropped by the selectors after the series defeat to Sri Lanka last year, with Eoin Morgan leading the team in the World Cup. But they flopped badly, failing to qualify from their group.
Cook is back in charge for the Tests in the West Indies, and he finished the first day of the first warm-up game against a St Kitts and Nevis Invitational XI unbeaten on 95, leaving him on the verge of scoring his first England century for almost two years.
And Grayson believes Cook is reaping the rewards of grafting during pre-season with Essex as he battled back from the disappointment of losing the England ODI captaincy.
???He???s been training with the boys for two or three weeks since January and he???s looked very refreshed and focused,??? Grayson told Sky Sports News HQ.
???I think with hindsight it was the wrong decision to drop him as England one-day captain and he was obviously very disappointed about that. But he???s had time to reflect and work on his game while he has been at home, spent some time with his family and friends, and he looks very fresh and focused.
???Obviously he got some runs yesterday which is good to see but he???s got a bigger test in front of him with the Caribbean tour and playing New Zealand and Australia to this summer. It was good to see him score some runs yesterday and get his confidence going.???
The LV= County Championship season begins on Sunday and Grayson is keen for Essex to rid themselves of their nearly-men tag after narrowly missing out on going up to Division One.
???We were eight points off the championship last year and our plan is to start the season as we finished last year,??? he said.
???I think we won six of our last seven Championship games and we got the record number of points for a team that wasn’t promoted, but all credit to Worcestershire and Hampshire last year. They pipped us right at the post so hopefully we can go one further this year and get promoted and win a one-day competition.
???We lost in two quarter-finals so we were the nearly men last year and we???d love to win something this year.???