A mechanism is examined by which cosmic rays may be accelerated to energies in the range 1015 to 1019 eV in the electric field of a shocked pulsar wind. The potential difference across the pole and the equator (as defined by the axis of rotation of the pulsar) of the wind is of the required magnitude. A cosmic ray entering the shock near the null at the pole can cross large regions of the wind before exiting the shock, thus gaining energy. Cosmic ray trajectories are calculated for a shock which is assumed to lie in a plane in Cartesian coordinates. Individual cosmic rays are found to gain energies of up to 1000 times their initial energy.