In order to determine an accurate and reliable high-pressure and high-temperature equation of state (EOS) of MgO, unified analyses were carried out for various pressure-scale-free experimental data sets measured at 1 atm to 196 GPa and 300-3700 K, which are zero-pressure thermal expansion data, zero-pressure and high-temperature adiabatic bulk modulus (K-S) data, room temperature and high-pressure KS data, and shock compression data. After testing several EOS models based on the Mie-Gruneisen-Debye description for the thermal pressures with the Vinet and the third-order Birch-Murnaghan equations for the 300-K isothermal compression, we determined the K'(T0) and gamma(V) using a new functional form gamma = gamma(0){1 + a[(V/V-0)(b)-1]} to express the volume dependence of the Gruneisen parameter. Through least squares analyses with prerequisite zero-pressure and room temperature properties of V-0, K-S0, alpha(0), and C-P0, we simultaneously optimized a set of parameters of K'(T0), gamma(0), alpha, and b required to represent the P-V-T EOS. Determined new EOS models of MgO successfully reproduced all the analyzed P-V-T-K-S data up to 196 GPa and 3700 K within the uncertainties, and the total residuals between calculated and observed pressures were found to be 0.8 GPa in root mean squares. These EOS models, even though very simple, are able to reproduce available data quite accurately in the wide pressure-temperature range and completely independent from other pressure scales. We propose these models for primary pressure calibration standards applicable to quantitative high-pressure and high-temperature experiments.