This work proposes to extract reliably the continuous distribution of orthopositronium (o-Ps) lifetimes in polymers from the positron annihilation lifetime spectra by solving a Fredholm integral equation using the maximum entropy method. The performance of the maximum entropy method (MELT) and the numerical Laplace inversion (CONTIN) methods for the reconstruction of the o-Ps annihilation lifetime distributions in polymers is compared using computer-simulated spectra. Both the MELT and CONTIN algorithms provide excellent estimates of the integrated intensities and the average lifetimes of o-Ps components in the simulated spectra. The width of the o-Ps lifetime distribution obtained by MELT is appreciably closer to the input value as compared with the result obtained by CONTIN, especially if the total number of counts in the data set is relatively low (N-0 = 2-4 million). The widths of o-Ps lifetime distributions obtained by MELT can be further modified and become even closer to the input value if we take into account the broadening of o-Ps lifetime distribution induced by some intrinsic factors in the simulation, for example, the finite statistics, range of lifetime grids, etc. MELT requires only relatively low statistics and does not need a reference spectrum with a single lifetime, which gives us the opportunity to reduce the measurement time and the possible negative influence of irradiation dose and the zero-time channel shift. The results in this work support the earlier conclusion based on the experimental evaluation that MELT is a powerful method for reconstruction of the o-Ps lifetime distribution in polymers (Nucl. Instrum. Methods B 1996, 117, 467-473).