Relativistic electron-positron winds with strong magnetic fields are considered as a source of radiation for cosmological gamma-ray bursters. Such a wind is generated by a millisecond pulsar with a very strong magnetic field. An electron-positron plasma near the pulsar is optically thick and in quasi-thermodynamic equilibrium. It is shown that most of the radiation from the pulsar wind is non-thermal and is generated in the following way. Kinetic energy, which is released in the process of deceleration of the neutron star rotation, is transformed mainly to magnetic field energy. The magnetic field is frozen in the outflowing plasma if the distance to the pulsar is smaller than approximately 10(13) cm. This field transfers the energy from the pulsar environment to the region outside the gamma-ray photosphere of the electron-positron wind. At a distance of more than approximately 10(13) cm, the magnetohydrodynamic approximation for the pulsar wind breaks down, and intense electromagnetic waves are generated. The frequency of these waves is equal to the frequency of the pulsar rotation. Outflowing particles are accelerated in the field of intense electromagnetic waves to Lorentz factors of the order of 10(6), and generate non-thermal synchro-Compton radiation. The typical energy of non-thermal photons is approximately 1 MeV. A high-energy tail of the gamma-ray spectrum may exist up to approximately 10(4) MeV. Baryonic matter is ejected occasionally from the pulsar magnetosphere. The baryonic matter ejection and subsequent suppression of the gamma-ray emission may be responsible for the time structure of gamma-ray bursts.