We present SHREC, an efficient algorithm for registration of 3D SPHARM (spherical harmonic) surfaces. SHREC follows the iterative closest point (ICP) registration strategy, and alternately improves the surface correspondence and adjusts the object pose. It establishes the surface correspondence by aligning the underlying SPHARM parameterization. It employs a rotational property of the harmonic expansion to accelerate its step for parameterization rotation. It uses a hierarchical icosahedron approach to sample the rotation space and searches for the best parameterization that matches the template. Our experimental results show that SHREC can not only create more accurate registration than previous methods but also do it efficiently. SHREC is a simple, efficient and general registration method, and has a great potential to be used in many shape modeling and analysis applications.