The spatiotemporal measurement of the ultrashort laser pulses is of great significance in the diagnosis of the instrument performance and the exploration of the laser and matter interaction. In this work, we report an advanced compressed ultrafast photography (CUP) technique to measure the spatiotemporal intensity distribution of the picosecond laser pulses with a single shot. This CUP technique is based on a three-dimensional image reconstruction strategy by employing the random codes to encode the space-time-evolving laser pulse and decode it based on a compressed sensing (CS) algorithm. In our CUP system, the measurable laser wavelength depends on the spectral response of the streak camera, which can cover a wide range from ultraviolet (200 nm) to near infrared (850 nm). Based on the CUP system we develop, we successfully measure the spatiotemporal intensity evolutions of some typical laser pulses, such as the 800 nm picosecond laser pulse, the 800 and 400 nm two-color picosecond laser pulses and the supercontinuum picosecond laser pulse. These experimental results show that the CUP technique can well characterize the spatiotemporal intensity information of the picosecond laser pulses. Moreover, this technique has the remarkable advantages with the single shot measurement and without the reference laser pulse.