We generate the equation of state (EOS) of solid parahydrogen (para-H2) using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor potential energy curve for the para-H2 dimer. The EOS curves for the fcc and hcp structures of solid para-H2 near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid para-H2, we eliminated by extrapolation the systematic errors associated with the choice of simulation parameters used in the PIMC calculation. We also investigate the temperature dependence of the EOS curves, and the invariance of the equilibrium density with temperature is satisfyingly reproduced. The pressure as a function of density and the compressibility as a function of pressure are both calculated using the obtained EOS and are compared with previous simulation results and experiments. We also report the first ever a priori prediction of a vibrational matrix shift from first-principles two-body potential functions, and its result for the equilibrium state agrees well with experiment.