This paper proposes a weighted average iterative closest point (ICP) algorithm (WA-ICP) to register multiple 3D surfaces. The new algorithm aims to tackle ambiguous correspondence and clearly improves the efficiency and reliability of 3D surface registration. We developed the WA-ICP theory, implemented the algorithm and evaluated its performance on two typical groups of surface samples. The performance of our new method is compared with both traditional ICP and weighted ICP. We also integrate a more elaborate scheme using normals for comparison. Our experiments show that WA-ICP has a good quality of convergence rate especially in the early iterations. The algorithm is also validated to be robust to low resolution and noise perturbation of 3D surfaces. Despite its simple form, the proposed WA-ICP clearly shows improved performance and some robust characteristics.