A Gibbs free energy equation of state (EoS) for phase I of solid methane has been developed with an original functional form. The EoS has a validity range from 21 to 300 K and up to 5000 MPa. The EoS parameters have been regressed on the literature data of molar volume, isothermal compressibility, thermal expansion, and isobaric and isochoric heat capacity. To the knowledge of the authors, this EoS is the most complete published model for phase I of solid methane in terms of the number of data of different thermodynamic properties used for the regression of the parameters and extension of the temperature and pressure validity range. The EoS represents the thermodynamic data within their estimated experimental uncertainty, and it maintains a physically correct behavior when extrapolated to high temperatures and pressures. The developed EoS for solid methane has been coupled with the reference equation of state for the fluid phases developed by Setzmann and Wagner in 1991 for calculating the melting and sublimation curves, and the predictions are in good agreement with the available data.