To investigate the mechanism of vortex motion, a pitched synthetic jet is arranged on the bottom of a cross flow and simulated by incompressible Naiver–Stokes equations with large eddy simulation. The Liutex vector identification method is utilized to quantitatively study the rotation strength and the core size of the vortex structures according to various driving frequencies ( St = 0.25, 0.5, 0.75, 1.0) and amplitudes ( A0 = 1.0, 1.5, 2.0, 2.5) of the synthetic jet during 21 periods. The results show that both the frequency and the amplitude play a significant role in the vortex generation mechanism of the synthetic jet. However, the amplitude makes a positive contribution to the rotation strength and the vortex core size, while the frequency makes a negative contribution. The vortex motion mechanism of a synthetic jet in a cross flow can be summarized as follows: low frequency and small amplitude favor the primary clockwise vortex, while high frequency and large amplitude motivate the anticlockwise vortex generation.