As deep neural networks (DNNs) have been success-fully developed in many applications with continuously increasing complexity, the number of weights in DNNs surges, leading to consistent demands for denser memories than SRAMs. RRAM-based in-memory computing (IMC) achieves high density and energy-efficiency for DNN inference, but RRAM programming remains to be a bottleneck due to high write latency and energy consumption. In this work, we present the Progressive-wRite In-memory program-VErify (PRIVE) scheme, which we verify with an RRAM testchip for IMC-based hardware acceleration for DNNs. We optimize the progressive write operations on different bit positions of RRAM weights to enable error compensation and reduce programming latency/energy, while achieving high DNN accuracy. For 5-bit precision DNNs, PRIVE reduces the RRAM programming energy by 1.82×, while maintaining high accuracy of 91.91% (VGG-7) and 71.47% (ResNet-18) on CIFAR-10 and CIFAR-100 datasets, respectively.