We present a quasiparticle self-consistent GW (QSGW) implementation for periodic systems based on crystalline Gaussian basis sets. Our QSGW approach is based on a full-frequency analytic continuation GW scheme with Brillouin zone sampling and employs the Gaussian density fitting technique. We benchmark our QSGW implementation on a set of weakly correlated semiconductors and insulators as well as strongly correlated transition metal oxides, including MnO, FeO, CoO, and NiO. The band gap, band structure, and density of states are evaluated using finite size corrected QSGW. We find that although QSGW systematically overestimates the bandgaps of the tested semiconductors and transition metal oxides, it completely removes the dependence on the choice of density functionals and provides a more consistent prediction of spectral properties than G0W0 across a wide range of solids. This work paves the way for utilizing QSGW in ab initio quantum embedding for solids.