V:YAG crystal was investigated as a passive Q-switch of longitudinally diode-pumped microchip laser, emitting radiation at wavelength 1030.5 nm. This laser was based on diffusion bonded monolith crystal (diameter 3 mm) which combines in one piece an active laser part (Yb:YAG crystal, 10 at.% Yb/Y, 3 mm long) and saturable absorber (V:YAG crystal, 2 mm long, initial transmission 86 % @ 1031 nm). The microchip resonator consisted of dielectric mirrors directly deposited on the monolith surfaces (pump mirror HT @ 968 nm and HR @ 1031 nm on Yb:YAG part, output coupler with reflection 55 % @ 1031 nm on the V:YAG part). For longitudinal CW pumping of Yb:YAG part, a fibre coupled (core diameter 100 μm, NA = 0.22, emission @ 968 nm) laser diode was used. The laser threshold was 3.8W. The laser slope efficiency for output mean in respect to incident pumping was 16 %. The linearly polarized generated transversal intensity beam profile was close to the fundamental Gaussian mode. The generated pulse length, stable and mostly independent on pumping power, was equal to 1.3 ns (FWHM). The single pulse energy was increasing with the pumping power and for the maximum pumping 9.7W it was 78 μJ which corresponds to the pulse peak-power 56 kW. The maximum Yb:YAG/V:YAG microchip laser mean output power of 1W was reached without observable thermal roll-over. The corresponding Q-switched pulses repetition rate was 13.1 kHz.