A spread spectrum signal demodulating method whereby spread-code synchronous acquisition and carrier synchronous acquisition are performed using FFT at high speed, wherein a received signal, of which the carrier wave is modulated with a signal obtained by spectrum- spreading data with a spread code, is subjected to the FFT and the result of the FFT is stored in a first memory. The FFT result of the received signal stored in the first memory and the result of FFT of the spread code stored in a second memory are read out and multiplied to detect the correlation between the received signal and the spread code. A readout address of either the FFT result of the received signal or the FFT result of the spread code is shifted by an amount corresponding to a carrier frequency of the received signal.