Electron swarm behaviour is studied, with particular emphasis on the anisotropy in velocity space, for the pulsed Townsend condition using a three-term approximation of the Boltzmann equation. The electron energy distribution and swarm parameters are calculated numerically considering elastic collisions only, with a cross-section of the form q( epsilon ) varies as epsilon r. Here epsilon is the electron energy. The calculation is performed with an electron-to-atom mass ratio, m/M, ranging from 10-4 to 10-2 at ratios of electric field to gas number density, E/N, of 2.8, 5.6 and 28 Td. The results show that the anisotropy represented by the ratio between the mean energies in the directions parallel and perpendicular to the field reaches about 6% at m/M=10-2 for r=-1/2 independent of E/N. Despite this anisotropy, swarm parameters such as the drift velocity, diffusion coefficient, mean energy and collision frequency deduced by the two-term calculation and those deduced by the three-term calculation agree with each other to within 0.3%. These facts show that the swarm parameters are insensitive to the anisotropy in the electron mean energy and the usual two-term analysis is fully valid for deduction of the swarm parameters as above, though the differences between the mean energies, and also the diffusion coefficients, parallel and perpendicular to the field cannot be predicted with the two-term analysis.