A boundary collocation method based on the least-square technique and a corresponding adaptive computation process have been developed for the plate bending problem. The trial functions are constructed using a series of the biharmonic polynomials, and the local error indicators are given by the residuals of the energy density on the boundary. In comparison with the conventional collocation methods, the solution accuracy in the present method can be improved in an economical and efficient way. In order to demonstrate the efficiency and advantages of the adaptive boundary collocation method proposed in this paper, two numerical examples are presented for circular plates subjected to uniform loads and restrained by mixed boundary conditions. The numerical results for the examples show good agreement with ones presented in the literature.