Concerning the problem that deadzone quantization in image compression cannot protect the edges of images effectively, a novel quantization algorithm called Lowpass subband Maxima Mapping Quantization (LMMQ) was proposed. In all kinds of subbands after wavelet transform, the importance of the coefficients in lowpass subbands could be decided by the average value of all coefficients in highpass subbands which have a mapping relationship with the coefficients in lowpass subbands. During quantization, the coefficients of highpass subbands were quantized by deadzone quantization in JPEG2000. The quantization step size of coefficients in lowpass subbands could be adaptively refined because of their own importance, so the edges of images could be protected effectively. The proposed algorithm has an advantage of adaptability in the aspect of coefficient selection when the step size is refined, and has higher encoding speed in Tier1 of EBCOT (Embedded Block Coding with Optimized Truncation) than traditional JPEG2000. The experimental results show that the proposed algorithm has an advantage of protecting the edges of images and has 0.2 dB more than traditional deadzone quantization.