A pulsed, single longitudinal mode, wavelength-tunable Tm:YAP laser is reported. We demonstrate 1 kHz stable operation with 230 µJ, 50 ns pulses and a spectrum linewidth narrowed below 4 pm (FWHM) close to the Fourier transform limit by use of a volume Bragg grating and a YAG etalon. The output wavelength was tuned from 1940 to 1960 nm owing to a transverse chirp of the period of the Bragg grating.