We study strip packing, which is one of the most classical two-dimensional packing problems: given a collection of rectangles, the problem is to find a feasible orthogonal packing without rotations into a strip of width 1 and minimum height. In this paper we present an approximation algorithm for the strip packing problem with absolute approximation ratio of 5/3+eps for any eps>0. This result significantly narrows the gap between the best known upper bound of 1.9396 by Harren and van Stee and the lower bound 3/2.