In this paper, we consider the robust secure beam-former design for multiple-input-single-output wiretap channels. Assuming that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and the secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceed certain thresholds with high probability. Therefore, including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem nonconvex and, hence, difficult to solve. In this paper, we investigate the outage probability constrained secrecy rate maximization problem using a novel two-step approach. Under a wide range of uncertainty models, our developed algorithms can obtain high-quality solutions, sometimes even exact global solutions, for the robust secure beamformer design problem. Simulation results are presented to verify the effectiveness and robustness of the proposed algorithms.