The differential energy spectrum of galactic cosmic rays in the vicinity of the Earth can be parameterized by the so-called force field model which has only one parameter, the modulation potential $phi$, for a given local interstellar spectrum. Here we present the series of monthly values of the modulation potential $phi$ since February 1951, reconstructed using the data from the worldwide neutron monitor network and calibrated with precise balloon and space-borne direct measurements of cosmic ray energy spectrum. This work provides a long series of a parameter allowing for a quantitative estimate of the average monthly differential energy spectrum of cosmic rays near the Earth. A comparison with other occasional direct measurements of cosmic ray spectra confirms the reliability of the present reconstruction. The results can be applied in studies of long-term solar-terrestrial relations and the global evolution of the heliosphere.