Hart, one of the shining lights when City won the Premier League in 2012, was criticised last year by former manager Roberto Mancini.
He also proved less than safe this week when he allowed a shot from Scotland's James Morrison to squirm off his arm and into the net during England's 3-2 friendly victory at Wembley.
Pellegrini told a news conference before their opening match of the season at home to Newcastle United on Monday that he had not spoken to Hart about his form.
"But I think Joe Hart has to demonstrate why he is the best goalkeeper of England every week he plays. He is a very important goalkeeper, I have a lot of trust in him, " he said.
"Everyone can make an error in one match. I am sure he will again this year demonstrate why he is the number one in England."
With strikers Stevan Jovetic and Alvaro Negredo added to Edin Dzeko and Sergio Aguero, City boast a formidable front line but Pellegrini shrugged off any potential selection problems.
"We have four important strikers, that is why they are here in this squad but we have four strikers for the whole season. I do not worry who plays tomorrow, next Monday or next Sunday.
"We have four strikers because I think we need four strikers. We will see each week which are the best of them for each match," said Pellegrini.
"I think we have the squad we need for the year, for important competitions - not only for the Premier League but also the Champions League so we have the squad we need." said the Italian.
- Sports & Recreation
- Joe Hart
- Premier League