A passively continuous-wave(CW) mode-locked Tm:YAP laser with a semiconductor saturable-absorber mirror was reported by using laser-diode as pump source. According to the ABCD matrix theory, the astigmatism and the stability in the cavity of the laser were theoretically analyzed. Stable continuous-wave mode-locked ps-pulses were achieved. The average output power of 0.73 W was obtained with the absorbed pump power of 7.96 W and the corresponding slope efficiency was 15.6%. The pulse duration was measured to be 1.7 ps with a repetition rate of 88.7 MHz at the central wavelength of 1 982.4 nm, and the corresponding slope efficiency was 15.6%. The results show that the Tm:YAP crystal has good thermal mechanical properties, which is very favorable for generating ultrashort pulses at around 2 μm.