The contribution of prompt cosmic-ray muons from charmed particles to the conventional muons from pi and K mesons is investigated. The inclusive cross sections for charmed-particle production are given in both non-diffractive and diffractive processes of primary-air collisions. The minimum contribution is determined by charmed-particle production only in non-diffractive processes. On the other hand, the maximum contribution is estimated by stressing the diffractive characters of the charmed particles produced. By solving the diffraction equations including the above cross sections, the energy spectra of the prompt cosmic-ray muons at sea level are given. The integral intensities of maximum and minimum prompt muons are equal to the vertical conventional one at about 15 and 290 TeV, respectively.