A two-stage compression framework for computer-generated hologram (CGH) with compressed sensing (CS) and quantum-inspired neural network (QINN) is proposed. A deep learning-based CS model is applied to sample the CGH at sub-Nyquist rates to generate measurements, and its more compact and representative information using interblock information is further extracted by QINN. With two-stage compression framework, the CGH is greatly compressed and suitable for storage and transmission. Experimental results demonstrate that our proposed two-stage compression framework can preserve more important holographic information during the compression, thus significantly improving the overall quality of reconstructed images compared to only using CS or QINN.