The Blues clinched the domestic double in their first season under Italian coach Carlo Ancelotti.
They could not go beyond the Champions League round of 16 though after losing 3-1 on aggregate to eventual winners Inter Milan.
"Last year we did the best. Every player did the best of their abilities and we want to do the same this year," Ancelotti said on Chelsea's official website on Saturday.
"We are able to do this and we can bring home some more trophies. We will start this season with the aim to win and the aim to be competitive until the end of the season.
"If we are able to win the Double again this year it will be fantastic, although obviously we want to do better in the Champions League as well."
Chelsea will open their new campaign on Sunday when they face Manchester United in the Community Shield, the season's annual curtain-raiser.