We present a study of methane moist convection on Neptune. We examine the stability conditions to initiate moist convection of methane clouds. Temperature lapse rates that are unstable to moist convection are subadiabatic by a factor of two or more while adiabatic and superadiabatic lapse rates are stable. In the observed Neptune temperature structure, vertical velocities ≥40 m s-1 are required to lift moist air above the stable region and initiate moist convection. Alternatively, moist convection could be initiated by air that is slightly drier than its surroundings. Moist convective clouds achieve altitudes up to 100 mb, thereby exceeding the temperature minimum and depositing methane in the Neptune stratosphere. We predict that at least 2000 such clouds pentrate the Neptune stratosphere per hour.