Study of the coupled harmonic oscillator is an important problem in quantum optics, and many actual physical problems are dependent on the model of the coupled harmonic oscillator, so the easy way to solve the coupled harmonic oscillator appears to be necessary. Through structuring a formal matrix by quadratic orthogonal mathematical theory and letting the Hamiltonian diagonalization of the n-dimensional anisotropic harmonic oscillators both coordinate and momentum coupling, its eigenvalues are obtained. The energy eigenvalue of three-dimensional coupled harmonic oscillator is solved by the method. The method does not need to derive the concrete form of the transformation matrix, which make it simple and easy to calculate the results to the eigenvalue problems of the Hamiltonian with symmetrical form.