In this paper, a lossy data compression for a sparse histogram image signal is proposed. It is extended from an existing lossless coding which is based on a lossless histogram packing and a lossless coding. We introduce a lossy mapping, which has less computational load than the rate-distortion optimized Lloyd-Max quantization, and combine it with a lossless coding. It was confirmed that the proposed method attains higher performance in the rate-distortion plane than existing methods. This is because it can utilize histogram sparseness of images, and also its inverse mapping does not magnify quantization noise.