With a certain intensity, a femtosecond laser focusing in the air will generate an air plasma and induce a shock wave. In order to study the propagation process of the shock wave, an ultrafast time-resolved vortex filtering imaging technique is introduced in this paper, and the observed dynamic process of the shock wave is analyzed. The shock wave from air plasma was observed when pumped by a 1.5 mJ femtosecond laser focused into the air through a lens, and the dynamic evolution of the shock wave in the period from 3-15 microseconds was analyzed. The results show that the femtosecond laser plasma air shock wave diffuses outwards in an asymmetrical spherical shape, and the propagation velocity is different along the laser propagation direction and behind the laser propagation direction, which are 372 m/s and 341 m/s, respectively. This observation is different from the traditional point explosion model, namely the symmetric case. We give a reasonable explanation for this asymmetric dynamic process.