We present the results of chemical modeling of complex organic molecules (COMs) under conditions typical for prestellar cores. We utilize an advanced gas-grain astrochemical model with updated gas-phase chemistry, with a multilayer approach to ice-surface chemistry and an up-to-date treatment of reactive desorption based on recent experiments of Minissale et al. (2016). With the chemical model, radial profiles of molecules including COMs are calculated for the case of the prototypical prestellar core L1544 at the timescales when the modeled depletion factor of CO becomes equal to that observed. We find that COMs can be formed efficiently in L1544 up to the fractional abundances of 10(-10) wrt. total hydrogen nuclei. Abundances of many COMs such as CH3OCH3, HCOOCH3, and others peak at similar radial distances of ~2000-4000 AU. Gas-phase abundances of COMs depend on the efficiency of reactive desorption, which in turn depends on the composition of the outer monolayers of icy mantles. In prestellar cores, the outer monolayers of mantles likely include large fractions of CO and its hydrogenation products, which may increase the efficiency of reactive desorption according to Minissale et al. (2016), and makes the formation of COMs efficient under conditions typical for prestellar cores, although this assumption is yet to be confirmed experimentally. The hydroxyl radical (OH) appears to play an important role in gas-phase chemistry of COMs, which makes it deserving further detailed studies.