A burst mode resonant power converter with high conversion efficiency has a rectifier, a power factor correction circuit, a resonant circuit, a controller, and a burst mode triggering unit. The maximum frequency switching end of the controller is connected to a maximum frequency variable circuit. When the load is medium or heavy, the maximum frequency variable circuit increases the maximum switch frequency of the controller. When the load is in the no-load or the light conditions, it reduces the maximum switch frequency thereof. Therefore, the controller reduces the number of times that the resonant circuit switches the bridge switch circuit. The conduction cycle of the 50% pulse signal output to the bridge switch circuit becomes longer. Larger energy can be transmitted at a time to the secondary coil of the transformer. This increases the overall efficiency.