The high-pressure behavior of the direct and indirect band gaps in zinc-blende-structure SiC is examined with use of self-consistent ab initio pseudopotential calculations. The fundamental band gap from GAMMA-15-nu to X1c is found to decrease linearly with pressure up to 200 kbar. This result disagrees with a recent experimental finding of strong sublinear behavior at pressures of 10 to 15 kbar. The linear pressure coefficients of the fundamental band pp and the transverse-optical-phonon frequency at the GAMMA-point in the Brillouin zone are in good agreement with measured values.