It's hard to measure the transient pulsed laser wavefront in inertial confinement fusion (ICF) system by the conventional methods for its short pulse width, large energy, high power and large distortion. An circular radial shearing interferometer based on spatial phase modulation is proposed to measure the transient near infrared laser pulse wavefront with high precision. Transient, highly precise measurement for near-infrared laser pulse wavefront, with pulse width of nanometer scale and central wavelength of 1064 nm, can be carried out with commonpath and no reference plane with round and rectangular aperture ranging from 30～150 mm. Theory of wavefront reconstruction has been validated by the computer simulation, and an error less than 1/1000λ is obtained. Compared with the results of ZYGO interferometer, an error less than 1/15λ for both peakvalley and root mean square value, is gained with good repeatability. The system has already been used in the ICF system to test the pulsed laser wavefront, and can also be applied to other visible and infrared lasers.