A transmission signal power control apparatus includes a power amplifier model unit which generates a learning digital signal by multiplying part of a predistortion signal by model coefficients which tentatively represent the input-output characteristics of a power amplifier, and an adaptive low-pass filter which generates a pseudo feedback signal by attenuating the high frequency components of the learning digital signal by multiplying the learning digital signal by weighting coefficients. Then, the power amplifier model unit updates the model coefficients such that the error between the feedback signal whose the high frequency components are attenuated by the low-pass filter and which is digitized, and the pseudo feedback signal is minimized, and the adaptive low-pass filter updates the weighting coefficients such that the error is minimized.