In the present paper, physical mechanism responsible for origin of streamwise vortices in mode A appeared in the three-dimensional (3-D) wake transition of a square-section cylinder is investigated. Direct numerical simulations at a Reynolds number of 180 firstly show that such streamwise vorticity is not originated from lateral surfaces. Then through the analysis of local flow field in the immediate neighborhood of rear surface, based on the theory of vortex-induced vortex, a new physical mechanism is identified. At first, the vertical vorticity on rear surface is generated by the intrinsic three-dimensional instability with the same instability wavelength of mode A. Then the streamwise vorticity at a specific sign is induced by such vertical vorticity, convected and concentrated in the shear layers. Finally, streamwise vortices are formed and shed with alternatively shedding spanwise vortices in the near wake. Moreover, the effect of induced spanwise vorticity on original two-dimensional (2-D) spanwise vorticity is also presented in detail.