A typical oleo-pneumatic shock-absorbing strut (classic traditional passive damper) in aircraft landing gear has a metering pin extending through the orifice, which can vary the orifice area with the compression and extension of the damper strut. Because the metering pin is designed in a single landing condition, the traditional passive damper cannot adjust its damping force in multiple landing conditions. Magnetorheological (MR) dampers have been receiving significant attention as an alternative to traditional passive dampers. An MR damper, which is a typical semi-active suspension system, can control the damping force created by MR fluid under the magnetic field. Thus, it can be controlled by electric current. This paper adopts a neural network controller trained by two different methods, which are genetic algorithm and policy gradient estimation, for aircraft landing gear with an MR damper that considers different landing scenarios. The controller learns from a large number of trials, and accordingly, the main advantage is that it runs autonomously without requiring system knowledge. Moreover, comparative numerical simulations are executed with a passive damper and adaptive hybrid controller under various aircraft masses and sink speeds for verifying the effectiveness of the proposed controller. The main simulation results show that the proposed controller exhibits comparable performance to the adaptive hybrid controller without any needs for the online estimation of landing conditions.