A distributed feedback Ti:sapphire laser (DFTL) pumped by a 532nm Q-switched pulse is proposed for the generation of tunable picosecond pulses. With coupled rate equation model, the temporal characteristics of DFTL are obtained. The numerical solutions show that the DFTL pulse with a 50-ps pulse duration and as much as 3.SmJ pulse energy can be obtained under 40-m J, 5-ns pulse pumping. The dependence of output pulse width on the laser crystal's length, pumping pulse duration, and pumping rate is also discussed in detail.