Point cloud registration is an important research problem in machine vision. One of the most widely used methods for point set registration is the iterative closest point (ICP) algorithm. However, ICP is known to be susceptible to local minima because it is based on the local iterative optimization technique and its performance critically relies on the quality of the initialization. To reduce the possibility of the algorithm falling into local minima, we propose an iterative algorithm based on geometric distance and local feature weighting named weighted correlation coefficient iterative closest point algorithm (WCC_ICP). The algorithm first establishes the corresponding relationship of points using linear representation and constructs an optimization model with constraints. Subsequently, the constrained optimization model is converted into an unconstrained optimization model by Lagrangian multiplication. Finally, an iterative technique is used to solve the optimal rigid body transformation of the optimized model. In addition, in each iteration, the identification ability of the local feature operator of points is used to repair the corresponding relation of points, which reduces the risk of the iterative algorithm falling into the local minima. Numerical experiments show that the proposed WCC_ICP algorithm reduces the risk of the iterative algorithm falling into local minima.