We study the eigenstate problem of a kind of coupled oscillators in the new quantum mechanical represen tation ｜q, μ, v〉, which is defined as the eigenvector of the operator (μQ + vP), where μ and v are two realparameters. We also use the U operator transformation method to deal with the same problem. We obtain the normally ordered product expressions of U operator and eigenvector. It is shown that the ground state of system Hamiltonian is a squeezed state.