The present invention relates to 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, the result being stored in a second memory, are read out and the results are multiplied to detect the correlation between the received signal and the spread code. During the detection of the correlation, 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 and the result is read from the first or second memory. The result of the multiplication is subjected to inverse FFT, thus detecting the correlation point between the received signal and the spread code.