The fourth-seeded Federer looked in complete control and saved the only break point he faced in the final game of the match with a forehand volley. He has yet to lose a set at the All England Club this year.
Federer, who owns 17 Grand Slam titles, lost in the second round at the All England Club in 2013, ending his streak of reaching the quarterfinals at 36 consecutive major tournaments.
He served 11 aces and hit 41 winners against Robredo, who defeated Federer in the fourth round of the U.S. Open last year.
The 23rd-seeded Robredo never has been past the fourth round at Wimbledon.