In this paper, we use a small bandwidth 808 nm cw Ti:sapphire laser as a pump source to pump a picosecond microchip laser. Different focal length pump focus lenses have been tested to improve laser efficiency. A maximum slope efficiency of around 20% is obtained by a 30 mm focal length lens. The pump threshold is only 13 mW. In order to reduce the timing jitter, we explored the self-injection seeding method by adding a seeding cavity to the microchip laser. A reduction factor in the timing jitter of up to a factor of 23 relative to the unseeded laser is obtained. From the experiments, we also found that higher seeding pulse energy will help to reduce the jitter more.