A sliding correlator is disclosed for establishing initial synchronization to spectrum-despread a received signal into a narrow band signal in a radio receiver in a spread spectrum CDMA system. The a sliding correlator can achieve high speed synchronization. A received signal is stored in a memory circuit (43). The received signal is read from the memory circuit (43) at a frequency substantially higher than the storing rate of the received signal. The read received signal is multiplied by a replica of a spreading code sequence by means of a multiplier (45), and the output signal of the multiplier (45) is accumulated by an accumulator (46) over a predetermined time period. The output of the accumulator (46) is decided by a threshold detector (47) whether or not it exceeds a predetermined threshold. When the output of the threshold detector (47) is less than the threshold, the phase of the spreading code sequence is shifted, and the detection is repeated. Since the correlation is taken by reading the received signal from the memory circuit (43) at a high speed, the initial synchronization can be established quickly.