A hybrid positron source which is based on the generation of channeling radiation by relativistic electrons channeled along different crystallographic planes and axes of a tungsten single crystal and subsequent conversion of radiation into e + e − -pairs in an amorphous tungsten target is described. The photon spectra of channeling radiation are calculated using the Doyle–Turner approximation for the continuum potentials and classical equations of motion for channeled particles to obtain their trajectories, velocities and accelerations. The spectral-angular distributions of channeling radiation are found applying classical electrodynamics. Finally, the conversion of radiation into e + e − -pairs and the energy distributions of positrons are simulated using the GEANT4 package.