In this paper, we present a robust beamforming (BF) scheme to improve the physical layer security (PLS) of a cognitive satellite terrestrial network (CSTN) at millimeter wave (mmWave) frequency. By employing the standard recommendations and the mmWave propagation model, a PLS framework is first defined for the CSTN in the presence of multiple eavesdroppers (Eves). A constrained optimization problem is then formulated to maximize the worst-case achievable secrecy rate of the cellular user subject to an allowable interference level for the satellite user. By expressing the imperfect Eve's channel state information (CSI) as a combination of many given angle-of-arrival (AOA) based discrete sets, we propose a method to transform the worst-case optimization problem into a min-max problem and then develop an iterative BF scheme to yield an analytical solution for the weight vectors. Finally, simulation results confirming the effectiveness and superiority of the proposed BF scheme are provided.