A simulation technique for analysis of transverse evolution of electron swarms in gases was developed based onmoment equations derived from the Boltzmann equation. A numerical calculation of the moment equations for an electron swarm was performed using a propagator method and it was demonstrated that the propagator method can be used to calculate the higher-order transverse diffusion coefficients stably. Applying a Hermite expansion technique, the electron distribution in real space and other electron swarm parameters were derived as functions of the transverse position. The calculation result was verified by comparisons with those by a Monte Carlo simulation and other methods. Features of the transverse electron swarm evolution were presented.