We consider quantum electrodynamics (QED) corrections to the fine splitting E(2P_{3/2})-E(2P_{1/2}) in the Li atom. We derive complete formulas for the mα^{6} and mα^{7}lnα contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results are in agreement with the most recent measurement, helping to resolve discrepancies between former ones and lay the foundation for the investigation of QED effects in light, many-electron atoms.