This letter investigates the secure transmission optimization in a multibeam satellite downlink network with multiple eavesdroppers, where each legitimate user is wiretapped by a corresponding eavesdropper. Our design objective is to maximize the sum secrecy rate of the multibeam satellite network in the presence of imperfect channel state information (CSI) of eavesdroppers, while guaranteeing the total transmit power constraint on-board the satellite. Due to the nonconvexity and intractability resulting from the eavesdroppers' CSI uncertainty, a robust beamforming scheme is proposed to transform the initial optimization problem into a convex framework by jointly applying the Taylor expansion, S-Procedure, and Cauchy-Schwarz inequality. Meanwhile, an iterative algorithm is introduced to obtain the optimal solution. Finally, the validity and superiority of the proposed scheme are confirmed through comparisons with the existing nonrobust and perfect CSI approaches.