The removal of multiples without simultaneously distorting primaries is one of the big challenges in seismic signal processing. This paper proposes a multiples prediction method, which estimate the multiples along their hyperbolic paths using the L1-norm based polynomial approximation. The primaries estimation is obtained by simply subtracting the predicted multiples from the original seismic data. Comparisons are made between the proposed method and the conventional L2-norm based polynomial approximation method. The results of both synthetic and seismic data show that the proposed method is very promising in practical applications.