Basing on numerical simulation of classical trajectories, the influence of a strong magnetic field on the rate of the spontaneous radiative recombination of antihydrogen atoms in cold antiproton-positron plasma is theoretically studied under the conditions of the ATHENA and ATRAP experiments carried out in CERN. The effect of the mag netic field is estimated by Monte-Carlo calculation of the change in the cross section of the positron hitting the near-nucleus region with the radius typical for the atomic ground state.