The hybrid radial boundary node method is applied to solve the biharmonic problems. Based on modified variational principle, the variational formula of the biharmonic problems is established. The radial basis point interpolation is employed to approximate the boundary variables, while the domain variables are interpolated by a combination of the fundamental solution of the laplace equation and the biharmonic equation. Compared to the regular hybrid boundary node method, as the shape function has the delta function property, the boundary conditions of the original problem can be easily implemented, and the fictitious source points are not involved. Numerical examples show that this method is efficient for solving the biharmonic equation.