A Novel dictionaries preconditioning algorithm for compressive sensing is proposed in this paper. This algorithm uses alternating projection method to construct sensing and measurement dictionaries with low mutual and cumulative cross coherence. The coherence property of the constructed dictionaries is superior to those constructed by Schnass’ method and by Dictionaries Construction algorithm. The complexity and computation amount is lower than Dictionaries Construction algorithm. The constructed dictionaries improve the performance of OMP and SP algorithms.