Due to its good decorrelating properties, the wavelet transform is a powerful tool for signal analysis.The lifting scheme is an efficient algorithm to calculate wavelet transforms and it allows for the construction of second-generation wavelets.Furthermore all classical wavelets can be generated by the lifting scheme.In this paper, we combine the Haar, CDF(2,2) wavelets with the improved Haars wavelets, and then propose an adaptive wavelet transform method which can adaptively match the wavelet to a given signal.And the simulation results show that compared to classical wavelets, this adaptive wavelet transform has advantages of both Haar and CDF(2,2) wavelets and performs well for the smooth and edge-dominated regions.