We investigate the ground state crystalline structure of nuclear matter in the ω-meson variant of the Skyrme model. After minimizing energy with respect to variations of both the Skyrme field and the period lattice, we find four distinct periodic solutions which are similar to those found in the standard Skyrme model. We use these crystals to calculate coefficients in the Bethe-Weizsäcker semi-empirical mass formula and the compression modulus of infinite nuclear matter, and find a significant improvement as compared with other variants of the Skyrme model.