We present an efficient multiresolution block sampling-based texture synthesis algorithm that works well for a wide variety of challenging textures. We consider the texture synthesis as a procedure that first estimates and then resamples a probability function. To achieve the effect of good and fast estimation of the probabaility function for a given texture as well as to retain the structural information during synthesis, we propose a concept of block sampling and a corresponding novel scheme of texture synthesis based on multiresolution block sampling (MBS). The computational complexity of the proposed algorithm is much lower than that of existing algorithms. Experimental results have shown that this novel texture synthesis algorithm produces superior results for many challenging textures.