An efficient adaptive multiresolution finite difference scheme is developed for hyperbolic conservation laws. Based on discrete multiresolution analysis of numerical solution on a nested grid structure,the scheme builds up an one-to-one relationship between wavelet coefficients with multiple nested grid point. At grid points where magnitude of wavelet coefficients are great,high-order WENO scheme is used for time evolution. While in the rest computational region,we use polynomial interpolation directly. Numerical experiments show that the method can reduce CPU time significantly,while maintaining accuracy and resolution of original regular grid method.