Registration of point clouds is one of the key technology of optical three-dimensional (3D) profilometry. Registrations without markers are always realized by using iterative closest point (ICP) algorithm. To improve the performance of ICP algorithm, an improved ICP algorithm based on the biunique correspondence of point clouds is proposed. The establishment of biunique point pairs is introduced, and the transformation of coordinates between point clouds are derived. By using a handheld 3D scanner to scan a statue consisting of high-frequency and low-frequency profiles, then 92 frames of point clouds are obtained. Using the proposed improved ICP algorithm, 82 frames of point clouds are successfully registered. Three representative variants of ICP are applied to register these 92 frames for comparison. Experimental results demonstrate that the proposed algorithm has advantages of strong robustness, high convergent speed and high convergent accuracy, which is useful for fast reconstruction of 3D models.