Based on the work of Luo & Melrose from the early 1990s, a maser curvature emission mechanism in the presence of curvature drift is used to explain the optical pulsations from anomalous X-ray pulsars (AXPs). The model comprises a rotating neutron star with a strong surface magnetic field, i.e. a magnetar. Assuming the space-charge-limited flow acceleration mechanism, in which the strongly magnetized neutron star induces strong electric fields that pull the charges from its surface and flow along the open field lines, the neutron star generates a dense flow of electrons and positrons (relativistic pair plasma) by either two-photon pair production or one-photon pair creation resulting from inverse Compton scattering of the thermal photons above the pulsar polar cap (PC). The motion of the pair plasma is essentially one-dimensional along the field lines. We propose that optical pulsations from AXPs are generated by a curvature-drift-induced maser developing in the PC of magnetars. Pair plasma is considered as an active medium that can amplify its normal modes. The curvature drift, which is energy-dependent, is another essential ingredient in allowing negative absorption (maser action) to occur. For the source AXP 4U 0142+61, we find that the optical pulsation triggered by curvature-drift maser radiation occurs at the radial distance R(nu(M)) similar to 4.75 x 10(9) cm to the neutron star. The corresponding curvature maser frequency is about nu(M) approximate to 1.39 x 10(14) Hz, and the pulse component from the maser amplification is about 27 per cent. The result is consistent with the observation of the optical pulsations from AXP 4U 0142+61.