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Transmission power control (TPC) leads to heterogeneous transmission power levels of the nodes in multi-hop wireless ad hoc networks. This eventually results in a quite complicated collision scenario due to hidden and exposed terminal problems, and brings a big challenge for analyzing the saturation throughput of the flows. This paper presents a saturation throughput model for IEEE 802.11 multi-hop ad hoc networks with heterogeneous transmission powers. In the model, one tagged node goes through with three processes, i.e., backoff, freezing and transmission, and each of which is composed of a certain number of continuous fixed length time slots. We put forward a four-dimensional Markov chain model for the behavior of the tagged node in each fixed-length time slot. Under the condition of heterogeneous transmission powers, we consider two types of collisions, i.e., the instantaneous and persistent collisions. Their probabilities are characterized by the one-step transition probability matrix of the Markov chain. The per-flow saturation throughput of the flow is eventually derived through an iterative way. Finally, the accuracy of our model is validated by comparing the analytical values and the simulation results, and the impact of the heterogeneous power levels on the performance of the wireless multi-hop ad hoc networks is effectively analyzed.