We report the first demonstration of femtosecond operation in a diode-pumped Yb-doped GdYSiO5 (Yb:GYSO) laser. With a semiconductor saturable absorber mirror for passive mode locking and a pair of SF6 prisms for intracavity dispersion compensation, we realized stable passive mode locking with the new Yb-doped laser material. Femtosecond pulses as short as 324 fs were obtained at the central wavelength of 1091 nm. The maximum average power is 450 mW for an absorbed pump power of 2.8 W, with a slope efficiency of 18.5% and a pulse repetition frequency of 80.1 MHz.