Cook has been facing calls to be replaced as both Test and one-day captain after struggling for runs in both formats against 50-over world champions India.
However, he remained Test skipper and last week, was also confirmed as captain for the 2015 World Cup in Australia and New Zealand.
Sport24 quoted Anderson, as saying at the Professional Cricketers' Association awards ceremony in London earlier this week that from the players' point of view, Cook is the best man to lead them at the World Cup.
He acknowledged that Cook had experienced more low points than most this summer, but for him to come through that spell spoke a lot about his character and the way he handled the criticism.
England lost both Test and one-day series with Sri Lanka on home soil before recovering from 1-0 down to beat India 3-1 in a five-match Test series, only to lose the one-day international campaign by the same margin.
England have lost five of their last six ODI series and few outside the camp expect them to win the World Cup, but Anderson said the two series against Sri Lanka and against Australia and India, would give the squad a good chance of preparing well for the World Cup.