In order to provide wireless services for wide sea area, this paper designs an integrated satellite-terrestrial maritime communication framework. Specifically, the terrestrial base station (TBS) serves near-shore users, while the low earth orbit (LEO) satellite communicates with off-shore users. We aim to improve the overall performance of integrated satellite-terrestrial maritime communication system. Thus, it makes sense to jointly optimize transmit beamforming at the TBS and LEO satellite. Due to sea wave fluctuation, the obtained channel state information (CSI) is often imperfect. In this context, a robust beamforming design algorithm is proposed with the goal of minimizing the total power consumption of integrated satellite-terrestrial maritime communication system while satisfying quality of service (QoS) requirements. Both theoretical analysis and simulation results confirm the effectiveness of proposed algorithm in maritime communications.