Vectorial analysis is done for Kukhtarev equations describing the nonvolatile holographic recording in doubly doped crystals, and the bulk photovoltaic effect and external electrical field are considered. On the basis of small signal approximation, the vectorial analytic solutions to the space-charge field for two-center holographic recording in the recording and readout phases are deduced. Considering the anisotropy of the space-charge field and effective electro-optic coefficient, an optimal recording direction of the two-center holographic recording is given. The optimal recording direction is determined mainly by the effective electro-optic coefficient, in (Fe, Mn):LiNbO3 crystal recording with 633 nm ordinary polarization beams, and the grating vector has a 22° angle to the optical axis and a 30° azimuth angle to x axis. But the optimal recording direction is determined mainly by the fixed space-charge field, in (Fe, Mn):LiNbO3 crystals recording with 633 nm extraordinary polarization beams, and the grating vector has a 44° angle to the optical axis and a 90° azimuth angle to x axis.