Ab initio pseudopotential calculations of the pressure dependence of the direct and indirect band gaps in diamond using a plane-wave and a local-orbital method are presented. The pressure derivative of the fundamental gap is found to be positive, in contrast with the negative derivative usually observed near the X point in the diamond- and zinc-blende-structure semiconductors. Its value is found to be 0.53 meV/kbar for the local-orbital method and 0.58 meV/kbar for the plane-wave method, as compared to the measured value of 0.5 meV/kbar. The anomalous sign of the pressure derivative of the fundamental gap is understood in terms of the absence of d states with the same principal quantum number as the low-lying s and pvalence states of the carbon atom.