3D surface matching would be an ill conditioned problem when the curvature of the object surface is either homogenous or isotropic, e.g. for plane or spherical types of objects. A reliable solution can only be achieved if supplementary information or functional constraints are introduced. In a previous paper, an algorithm for the least squares matching of overlapping 3D surfaces, which were digitized/sampled point by point using a laser scanner device, by the photogrammetric method or other techniques, was proposed [Gruen, A., and Akca, D., 2005. Least squares 3D surface and curve matching. ISPRS Journal of Photogrammetry and Remote Sensing 59 (3), 151-174.]. That method estimates the transformation parameters between two or more fully 3D surfaces, minimizing the Euclidean distances instead of z-differences between the surfaces by least squares. In this paper, an extension to the basic algorithm is given, which can simultaneously match surface geometry and its attribute information, e.g. intensity, colour, temperature, etc. under a combined estimation model. Three experimental results based on terrestrial laser scanner point clouds are presented. The experiments show that the basic algorithm can solve the surface matching problem provided that the object surface has at least the minimal information. If not, the laser scanner derived intensities are used as supplementary information to find a reliable solution. The method derives its mathematical strength from the least squares image matching concept and offers a high level of flexibility for many kinds of 3D surface correspondence problem.