Processing in-memory (PIM) is promising to accel- erate neural networks (NNs) because it minimizes data movement and provides large computational parallelism. Similar to machine learning accelerators, application mapping, which determines the operation scheduling and data layout, plays a critical role in the NN acceleration on PIM. The mapping optimization of previous NN accelerators focused on optimizing the latency of sequential execution. However, PIM accelerators feature a distinct design space of application mapping from conventional NN accelerators, due to the spatial execution of NN layers across different memory locations. This enables opportunities for overlapping execution of consecutive NN layers to improve the latency, where the succeeding layer can start execution before the preceding layer fully completes the computation. In this paper, we propose Fast-OverlaPIM framework that incorporates the computational overlapping optimization into the DNN mapping exploration pro- cess on PIM architectures. Fast-OverlaPIM includes analytical algorithms for fast and accurate overlap analysis. Furthermore, it proposes a novel mapping search strategy and a transformation mechanism to enable efficient design space exploration on the overlap-based mapping for the whole network. Our framework demonstrates a significant improvement in runtime performance from 3.4× to 323.1× compared to the previous state-of-the- art overlap-based framework. Our experiments show that Fast- OverlaPIM can efficiently produce mappings that are 4.6× to 18.1× faster than the state-of-the-art mapping optimization framework under the same architecture constraints.