We calculate the high-energy component of the atmospheric neutrino flux which arises from decays of the charmed particles. Cross sections of the D mesons and Λ c + baryons production in pA and πA collisions are calculated within the framework of the quark-gluon string model (QGSM). The recent data on the cross sections of charmed meson production at high energies, obtained in experiments at the LHC, allow an improvement of the QGSM free parameters and new estimate of the prompt atmospheric neutrino flux. The newly-calculated flux of the prompt neutrinos is three times smaller than the flux predicted with the previous version of QGSM. We compare our result with the constraint derived from IceCube experiment as well as with predictions obtained with different charm production models.