The recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999); ibid. 114, 1467 (2001)] is extended to complex-symmetric Hamiltonians. It is shown that the complex-symmetric Lanczos algorithm possesses several useful numerical properties similar to those observed in real-symmetric cases, which enable one to compute multiple transition amplitudes with a single Lanczos propagation. The usefulness of the method is illustrated in calculating the S-matrix elements for the collinear H+H-2 reaction.