Assuming a damping force proportional to the velocity, it is shown that the usual quantum condition between the physical variables, namely the displacement and the momentum, has to be modified by the damping. However, it is possible to change to new variables which are canonical. Then we can apply the usual quantum mechanics and use the usual physical interpretation through the statistical average values. The case of a one-dimensional damped harmonic oscillator under the action of an arbitrary external force has been worked out as an example. No difficulty arises and the results are reasonable.