Understanding and reducing the influence of noise on the fidelity of transmitted particles is one of the important research directions in quantum teleportation. Different from the previously reported independent noise and the memory Pauli noise, the effect of memory amplitude damping noise on fidelity is investigated, and a method to resist this influence is proposed. According to this method, the fidelity can be improved by implementing the extra weak measurement and recover measurement before and after distributing particles respectively. The results show that, the memory factor strength of the memory amplitude damped channel is positively correlated with the fidelity. Moreover, the weak measurement and recovery measurement methods can also improve the fidelity of the transmitted particles to a certain extent in partial or full memory channels.