We propose an explicit numerical method for the periodic Korteweg–de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers’ nonlinearity. We prove first-order convergence in both space and time under a mild Courant–Friedrichs–Lewy condition τ=O(h), where τ and h represent the time step and mesh size for solutions in the Sobolev space H^3((−π,π)), respectively. Numerical examples illustrating our convergence result are given.