A cross section of the process e+ e− → π + π − π + π − has been measured using an integrated luminosity of 17 pb^{-1} collected with the CMD-3 detector in the center-of-mass energy range 650-1000 MeV. The main goal of this analysis is precise measurement of the cross section. High-precision measurements of various hadronic cross sections are of great interest in connection with the problem of the muon anomalous magnetic moment g-2. The e+ e− → π + π − π + π − can be used to test the conservation of vector current (CVC) hypothesis, which predicts a relation between the e+ e− → π + π − π + π − cross section and the spectral function for the τ − → π−π0π0π0 decay.