An efficient laser diode-pumped Yb:YGG laser is demonstrated by using a high quality Yb:YGG crystal grown by optical floating zone method, output power up to 1.95 W has been obtained under incident pump power of 6.7 W, corresponding to optical-to-optical efficiency of 29.1% and maximum slop efficiency of 60%. By using a semiconductor saturable mirror absorber (SESAM) to start and sustain the mode-locking, stable laser pulses of 2.1 ps has been obtained without dispersion compensation. The central wavelength is 1035 nm and the output power is 1 W, corresponding to optical-to-optical efficiency of 18.2%.