We demonstrate a diode-end-pumped passively mode-locked 1338 nm Nd:YAG laser with a semiconductor saturable absorber mirror. At the absorbed pump power of 8.89 W, an average output power of 1.12 W was obtained with a slope efficiency of 14%. The pulse width was 22.4 ps with a repetition rate of 63.9 MHz, corresponding to a peak power of 782 W. In addition, the bandwidth of the mode-locking spectrum is as narrow as 20.44 GHz, which shows the potential application in long-distance ranging and fiber information transmission because of the low dispersion of these ultrashort pulses.