Learned Image Compression (LIC) gradually became more and more famous in these years. The hyperprior-module-based LIC models have achieved remarkable rate-distortion performance. However, the memory cost of these LIC models is too large to actually apply them to various devices, especially to portable or edge devices. The parameter scale is directly linked with memory cost. In our research, we found the hyperprior module is not only highly over-parameterized, but also its latent representation contains redundant information. Therefore, we propose a novel pruning method named ERHP in this paper to efficiently reduce the memory cost of hyperprior module, while improving the network performance. The experiments show our method is effective, reducing at least 22.6% parameters in the whole model while achieving better rate-distortion performance.