A master oscillator power amplifier (MOPA) pulsed laser operating at 1342 nm is demonstrated. It consists of an acousto-optical (A-O) Q-switched oscillator and two-stage Nd: YVO 4 power amplifiers. The spherical aberration self-compensation technique is used in the second stage amplifier to obtain high-beam-quality laser output. The maximum average output power of 20.4 W is obtained with the oscillator power of 2.0 W and the total pump light power of 184.08 W, corresponding to an optical-optical efficiency of 11.08%. The repetition rate and pulse width are 100 kHz and 14.8 ns, respectively. The beam quality factor is M x 2 =1.45 and M y 2 =1.34. According to our knowledge, this is the maximum output power with a pulse width of ten-nanoseconds level and repetition rate of one-hundred-kilohertz level by an A-O Q-switch at the wavelength of 1342 nm.