A picosecond GaInP/AlGaInP/GaAs vertical external-cavity surface-emitting laser (VECSEL) at 675 nm is reported. The laser is mode-locked with a GaInP/AlGaInP/GaAs saturable absorber mirror and emitted ~5.1 ps pulses at a 973 MHz repetition rate and an average power of 45 mW. To our knowledge, this is the first demonstration of a passively mode-locked VECSEL emitting fundamental laser radiation at the visible part of the spectrum.