We present a passively mode-locked Nd:YAG laser with 10.7-W average output power in a diffraction-limited beam. Stable self-starting mode locking with a pulse duration of 16 ps and a pulse energy of 120 nJ is obtained with a semiconductor saturable-absorber mirror. The laser is directly side pumped with two 20-W diode bars. Single-pass frequency doubling in an external 5-mm-thick KTP crystal yields 3.2-W average power at 532 nm.