[en] The propagator of multidimensional damped harmonic oscillator described by a non-selfadjoint Hamiltonian with complex potential was found earlier. The one-dimensional case is treated in detail with the following results. The non-damped limit gives correct propagator including Maslov phase factor. For some initial conditions, classical limit of the solution can differ from the behaviour of the classical damped oscillator, the difference being negligible in the case of weak damping. Point spectrum of the considered pseudo- Hamiltonian is found