A self-starting picosecond Ti:sapphire laser pumped by 465 nm blue laser diodes is introduced. A double-side pumping structure is adopted in the laser, which makes up for the lack of mode matching and makes full use of the Ti:sapphire crystal with low doping concentration and long optical length. When the pump power is 7 W, a continuous wave output power of 718 mW is achieved and no obvious pump-induced loss phenomenon is observed. With the assistance of semiconductor saturable absorber mirror (SESAM), the self-starting passive mode-locking output of 371 mW and 6 ps is obtained, and the RMS value of the output power is less than 0.5% within 10 hours.