The RF power amplifier circuit including multiple amplification stages has a previous-stage amplifier, a next-stage amplifier and a controller. The previous-stage amplifier responds to an RF transmission input signal. The next-stage amplifier responds to an amplification signal output by the previous-stage amplifier. In response to an output-power-control voltage, the controller controls the former- and next-stage amplifiers in quiescent current and gain. In response to the output-power-control voltage, the quiescent current and gain of the previous-stage amplifier are continuously changed according to a first continuous function, whereas those of the next-stage amplifier are continuously changed according to a second continuous function. The second continuous function is higher than the first continuous function by at least one in degree. The RF power amplifier circuit brings about the effect that the drop of the power added efficiency in low and middle power modes is relieved.