We propose and demonstrate nonlinear amplifications of self-accelerating Airy beams by two-wave mixing in photorefractive crystals both numerically and experimentally. By employing a broad Gaussian beam as the pump beam, we show that weak signal Airy beams can be significantly amplified under both diffusion and drift mechanisms. It is revealed that not only higher optical gains but also faster response time can be achieved in the presence of an external electric field, where the drift mechanism dominates. We verify that the self-accelerating and self-healing characteristics of the Airy beams are well preserved during the nonlinear amplification. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement