We present calculations of the equilibrium volume and bulk modulus for \ensuremath{\alpha}-Ce. The calculations are based upon the local-spin-density approximation (LSDA) and the generalized-gradient approximation (GGA). These calculations are done with a full-potential linear-muffin-tin-orbital method. The equilibrium volume, which generally is too low in LSDA calculations, is improved considerably for \ensuremath{\alpha}-Ce by the gradient correction. The increase of the equilibrium volume, when the gradient corrections are considered, results in a decrease of the bulk modulus, which therefore also becomes in better agreement with experiment. It is shown that by neglecting the nonsphericity of the electron charge density and the potential, a fortuitous improvement of the equilibrium volume and bulk modulus of \ensuremath{\alpha}-Ce is obtained. The full-potential GGA calculations for \ensuremath{\alpha}-Ce show an accuracy relative to experiment that is comparable to what is found for corresponding calculations for a d-transition metal. The equation of state for \ensuremath{\alpha}-Ce is well reproduced by the full-potential GGA calculations in the pressure range for which there is data available (0--500 kbar).