The effects of AlAs acoustical and optical phonons on the tunneling current in an ideal GaAs-AlAs-GaAs-AlAs-GaAs structure are discussed. The transfer Hamiltonian method was extended to inelastic tunneling current in a double-barrier structure. It is found that the current off resonance in the Tsu-Esaki model could be enhanced by orders of magnitude by inelastic tunneling due to the coupling of electrons to barrier optical phonons. The contribution to the current due to the deformation-potential coupling of electrons to barrier acoustical phonons is found to be much less important.