The interaction between galaxies is believed to be the main origin of the peculiarities of galaxies, which disturbs not only the morphology but also their kinematics. These disturbed and asymmetric features are the indicators of galaxy interaction. We study the velocity field of the ionized gas of the paired galaxies in the SDSS-IV MaNGA IFU survey. Using the kinemetry package, we fit the velocity field of the ionized gas to quantify the degree of kinematic asymmetry. We find that the star formation rate (SFR) of the paired galaxies with high kinematic asymmetry is significantly enhanced even when the projected separation between the pair members is quite large (dp ∼ 100 h-1 kpc. On the contrary, no significant SFR enhancement is found for the paired galaxies with low kinematic asymmetry even when their projected separation is small (dp < 30 h-1 kpc). Moreover, we also find that the fraction of galaxies with high kinematic asymmetry is much higher in close pairs (dp < 30 h-1 kpc) than those with larger d<SUB<p, which explains well the early statistical finding of the significant SFR enhancement in close pairs. Our new findings illustrate that the kinematic asymmetry is an excellent indicator of galaxy-galaxy interaction strength, which helps us better understand the merging stage of the observed galaxy pairs.