A ridgelet kernel regression method is presented in this paper to approximate multi-dimensional functions, especially those with certain kinds of spatial inhomogeneities. This method is based on ridgelet theory, kernel and regularization techniques from which we can deduce a regularized kernel regression form. By representing this form with quadratic programming and taking the obtained solution to define a fitness function, we use particle swarm optimization to optimize the directions of ridgelets. The properties of ridgelet can guarantee the stability of this method in approximating multi-dimensional functions, as well as its superiority for functions with linear singularities. Additionally, the regularized technique employed in this model leads to smaller generalization error. Experiments in the tasks of regression and classification show its effectiveness.