State-selective single electron capture in He2+-He collisions at energies ranging from 20 to 40 keV have been studied experimentally by means of cold target recoil ion momentum spectroscopy. The differential cross sections have been obtained by measuring the longitudinal and transverse momenta of recoil ions. The results show that single electron capture into L shell is the dominant reaction channel, which was qualitatively explained with reaction window theory. The measured state-selective cross sections agree with the semi-classical close-coupling calculations, but have some deviations from the results of photon emission measurement. Total angular differential cross sections show that the single electron capture into ground state mainly contributes at small angles, and the single electron capture into excited states contributes at large angles. The oscillating structures of angular differential cross sections are observed, and can be understood by the interference of molecular orbits during the collision processes. The measured angular differential cross sections are compared with other experiments and the quantum-mechanical calculation.