Robshaw's leadership has come under criticism during the past 18 months, with the exiled Steffon Armitage mooted as a better option to lead the side.
However, with the World Cup less than a year away, Moody believes that the Harlequins flanker has earned the right to captain his country.
"There are always doubts and question marks for any captain, even if you're right at the races. Someone will always be saying there's a better player out there," he is quoted as saying by Sky Sports News.
"That's certainly something Chris has had to deal with in recent months. I don't think there's any question over his captaincy, he's earned that right over the last three years."
England return to action on November 8 when they welcome world champions New Zealand to Twickenham Stadium.