This paper presents a recursive weighted least-squares (RWLS) algorithm to jointly estimate carrier frequency offset (CFO) and timing offset (TO) for SC-FDE systems. The Zadoff-Chu (ZC) sequences are put ahead of each SC-FDE symbols as the unique words (UWs). Using the phase difference between the UWs of two consecutive symbols, the proposed method fits a straight line. The intercept and slope of the line are CFO and TO, which can be precisely estimated by weighted least-squares algorithm. It also makes good use of the previous estimated information, combined with current observation values, to compute recursively to obtain the final results. Simulation results show that the proposed algorithm can achieve similar performance as that of the weighted least-squares algorithm with lower computation complexity.