Path instability of a rising bubble is a complex phenomenon. In many industrial applications, bubbles encounter walls, and the interactions between the bubbles and the wall have a significant impact on flow physics. A single bubble rising near a vertical wall was experimentally observed to follow a bouncing trajectory. To investigate the near-wall dynamics of rising bubbles, 3D numerical simulations were performed based on the volume of fluid (VOF) method using the open source solver OpenFOAM. The effect of wall proximity and surface tension on the bubble trajectory was investigated. Previous studies have focused on the near-wall rising dynamics of bubbles for higher Eotvos numbers (Eo) and varied the Galilei number (Ga). The physical properties of the flow were chosen such that the free-rising bubble lies in the rectilinear regime. The Ga number was fixed and the Eo number was varied to analyze its effect on the bubble’s rising trajectory. It was found that the presence of the wall increases the drag experienced by the bubble and induces an early transition from rectilinear to a planar zigzagging regime. We identify the maximum wall distance and the critical Eo number for the bubble to follow a bouncing trajectory. The amplitude, frequency and wavelength of the bouncing motion are independent of the initial wall distance, but they decrease with decreasing surface tension.