Point set registration has been a topic of significant research interest in the field of mobile intelligent unmanned systems. In this paper, we present a novel approach for a three-dimensional scan-to-map point set registration. Using Gaussian process (GP) regression, we propose a new type of map representation, based on a regionalized GP map reconstruction algorithm. We combine the predictions and the test locations derived from the GP as the predictive points. In our approach, the correspondence relationships between predictive point pairs are set up naturally, and a rigid transformation is calculated iteratively. The proposed method is implemented and tested on three standard point set datasets. Experimental results show that our method achieves stable performance with regard to accuracy and efficiency, on a par with two standard methods, the iterative closest point algorithm and the normal distribution transform. Our mapping method also provides a compact point-cloud-like map and exhibits low memory consumption.