In photorealistic rendering, refraction is a vital optical phenomenon for transparent objects. This study proposes a real-time image-space method for approximate multiple refraction. First, a depth-peeling technique is used to disassemble a 3D polygonal model into four layers of normal and depth textures. Next, a modified ray-height-field intersection algorithm is employed to resolve discontinuities between the layers and compute the intersection, refraction, and total internal reflection. Finally, an environment map with a refraction vector is used to compute the final shading. The image space and shader technique enables generating a maximum of four bounces to increase the refraction detail and handle more complex scenes compared with those examined in previous methods. We performed several experiments with various scenes and the results showed the feasibility and quality of the proposed multi-refraction method. In addition, the rendering efficiency was demonstrated by comparing the proposed method with GPU-based ray tracing.