Due to rapid growth in image sizes, an alternate of numerically lossless coding named visually lossless coding is considered to reduce storage size and lower data transmission. In this paper, a lossy compression method on encrypted color image is introduced with undetectable quality loss and high compression ratio. The proposed method includes the Xinpeng Zhang lossy compression [1], Hierarchical Oriented Prediction (HOP)[2], Uniform Quantization, Negative Sign Removal, Concatenation of 7-bit data and Huffman Compression. The encrypted image is divided into rigid and elastic parts. The Xinpeng Zhang elastic compression is applied on elastic part and HOP is applied on rigid part. This method is applied on different test cases and the results were evaluated. The experimental evidences suggest that, the proposed method has better coding performance than the existing encrypted image compressions, with 9.645 % reductions in bit rate and the eye perception is visually lossless.