A lossless wavelet-based image compression method with adaptive prediction is proposed. Firstly, we analyze the correlations between wavelet coefficients to identify a proper wavelet basis function, then predictor variables are statistically test to determine which wavelet coefficients should be included in the prediction model. At last, prediction differences are encoded by adaptive arithmetic coding to achieve a higher-rate compression. Instead of relying on a fixed number of predictors on fixed locations in the traditional approaches, we proposed the adaptive prediction approach to overcome the multicollinearity problem. The proposed innovative approach integrating correlation analysis for selecting wavelet basis function with predictor variable selection is fully achieving high accuracy of prediction. Experimental results show that the proposed approach indeed achieves a higher compression rate on CT and MRI images comparing with several state-of-the-art methods.