The objective of this paper is to investigate the counterjet dynamics generated during the bubble rebound stage near a rigid boundary via both experimental and numerical methods. In the experiments, the temporal evolution of the bubble shapes and the formation of the counterjet are recorded by the high-speed camera. The results are presented for a single bubble generated near different normalized standoff distances γ = L/Rm from 0.5 to 3, where L is the distance between bubble center and boundary, and Rm is the maximum radius of bubble. In order to account for the generation mechanism of counterjet, a 3D weakly compressible model with reformulated mass conservation equation is proposed to predict the transient process of the single bubble patterns and its surrounding flow structure, including the velocity and pressure dynamics and the pressure waves around the bubbles. The results show that the counterjet, the fluid structure opposite to the high-speed jet in the propagation direction, forms during the rebound stage when 1 < γ < 3, and the maximum height of the counterjet increases first and then decreases with the increase of γ. Furthermore, the numerical results show that the generation of counterjet is related to the shock wave induced by bubble collapse. The tension wave causes a low-pressure region at the top of the stagnation ring, which is easy to generate the cavitation bubble. And those cavitation bubbles move upwards along the flow streaming generated inside the stagnation ring, which results in the counterjet.