We present a grain-fluid mixture for debris flows moving on a rugged (non-trivial) topography, where entrainment and deposition may take place. The model equations are derived with respect to a terrain-following coordinate system, which is constructed based on the topographic surface. The coordinates are fixed in space, and a “subtopography” is added on the coordinate surface to account for the variation in the local topography when entrainment or deposition takes place. Numerical implementation is made based on a GPU-accelerated simulation tool, into which the entrainment-deposition mechanism is integrated accordingly. Two numerical examples are assigned to investigate the key features of the proposed model. One is on a horizontal plane, on which a finite mass of grain-fluid mixture is released from the state of rest. In this example, debris flow deposits significantly impact the post-event} morphology and the associated flow behaviors. The other concerns a moving mass down an inclined chute merging into a horizontal deposition plane, where the levee formation is reproduced. At the end, the model is validated against a debris flow experiment to evaluate its applicability.