Provided are a hybrid power vehicle range extender power following control method and system. The method includes: when a vehicle satisfies range extender power closed-loop control conditions, an actual charge-discharge power of a power battery and a charge-discharge power expectation value of the power battery are taken as control errors to adjust a total range extender electric power requirement, an engine torque requirement is calculated according to the total range extender electric power requirement, and an engine is controlled to perform the engine torque requirement; and when it is detected that a drive motor electric power suddenly changes and/or a load power suddenly changes, engine quick torque control is activated, and an engine quick torque requirement is taken as a feed-forward value of a generator speed setting controller to control a generator.