This study proposes a three-dimensional vortex method for the simulation of bubbly flow. The method discretizes the vorticity field by vortex elements. The behavior of the vortex element and the bubble motion are simultaneously analyzed with the Lagrangian approach to compute the time evolution of the flow. This study also applies the vortex method to the simulation of a bubble plume to demonstrate the validity of the method. In a tank containing water, small hydrogen bubbles are released from the bottom of the tank. The bubbles rise due to the buoyant force and induce the water flow around them. The simulation for the plume at the starting period highlights that the rising bubbles induce large-scale eddies at their top and that the bubbles are entrained into the eddies. The simulation for the developed plume demonstrates that large-scale eddies appear around the rising bubbles and that they cause the meandering behavior of the plume. Such three-dimensional features of the bubble plume are favorably compared with the experimental results, indicating the validity of the proposed vortex method.