We demonstrate the Kerr-lens mode-locked Pr3+:LuLiF4 (Pr:LLF) laser pumped by a blue laser diode (LD). By theoretical calculation of the group velocity dispersion in the laser gain, the compensation was employed for the realization of the continuous-wave mode-locked laser at the wavelength of 604 nm with the pulse width of 1.1 ps which, to the best of our knowledge, is the shortest pulse width in the Pr3+ ion doped crystal lasers pumped with LDs. It can be believed that the present Pr:LLF laser should provide some inspiration for the development of the blue LD pumped visible lasers, especially in the mode-locking laser operation.