An innovative and effective algorithm is proposed to estimate the spread-spectrum sequence of a direct spread-spectrum sequence (DSSS) signal in non-cooperative communication systems. In particular, a measurement function, which is used for sequence synchronisation, and a detection statistic, which is for sequence estimation chip by chip, are developed based on the idea of correlation. Only linear complex addition and multiplication are required for the implementation of the algorithm. Theoretical analysis and computer simulations verify the effectiveness of the algorithm.