We have demonstrated that optical pulses as short as 38fs can be successfully generated from a simple linear-cavity dye laser. The laser consists of a six-mirror cavity with two dye jets (a gain jet with Rh 6G and a saturable absorber jet with DODCI) and a pair of prism as group-velocity disperesion compensator, and is synchronously pumped by the frequency-doubled output of a CW mode-locked Nd: YAG laser. The average output power is 20 mW at a reptition rate of 100 MHz.