Adaptive discrete wavelet transform based on the lifting scheme was introduced.The weighed coefficient of Bernstein filter predictor was determined to match adaptively with a desired signal by LMS criteria. The algorithm can be applied to signal denoise by the soft threshold of wavelet. Finally this method was extended to denosing of two dimension images. The numerical experiment shows that the method is a powerful method for denoising image. It can keep the character of edge and texture of the image. The advantages of lifting scheme Lie in its flexible design and simple comput .