Block compressed sensing (BCS) is a promising method for resource-constrained image/video coding applications. However, the quantization of BCS measurements has posed a challenge, leading to significant quantization errors and encoding redundancy. In this paper, we propose a quantization method for BCS measurements using convolutional neural networks (CNN). The quantization process maps measurements to quantized data that follow a uniform distribution based on the measurements’ distribution, which aims to maximize the amount of information carried by the quantized data. The dequantization process restores the quantized data to data that conform to the measurements’ distribution. The restored data are then modified by the correlation information of the measurements drawn from the quantized data, with the goal of minimizing the quantization errors. The proposed method uses CNNs to construct quantization and dequantization processes, and the networks are trained jointly. The distribution parameters of each block are used as side information, which is quantized with 1 bit by the same method. Extensive experiments on four public datasets showed that, compared with uniform quantization and entropy coding, the proposed method can improve the PSNR by an average of 0.48 dB without using entropy coding when the compression bit rate is 0.1 bpp.