Cognitive radio networks (CRNs) and millimeter wave (mmWave) communications are two major technologies to enhance the spectrum efficiency (SE). Considering that the SE improvement in the CRNs is limited due to the interference temperature imposed on the primary user (PU), and the severe path loss and high directivity in mmWave communications make it vulnerable to blockage events, we introduce an intelligent reflecting surface (IRS) into mmWave CRNs. Due to the estimation mismatch and the passivity of Eavesdroppers (Eves), perfect channel state information (CSI) of wiretap links is challenging to obtain, which promotes our research on robust secure beamforming (BF) design in the IRS-assisted mmWave CRNs. This paper considers the collaborate scenario of Eves, which allows us to investigate the BF design in the harsh eavesdropping environment. Specifically, by using a uniform linear array (ULA) at the cognitive base station (CBS) and a uniform planar array (UPA) at the IRS, and supposing that imperfect CSIs of angle-of-departures for wiretap links are known, we formulate a constrained problem to maximize the worst-case achievable secrecy rate (ASR) of the secondary user (SU) by jointly designing the transmit BF at the CBS and reflect BF at the IRS. To solve the non-convex problem with coupled variables, an efficient alternating optimization algorithm is proposed. Finally, simulation results indicate that the ASR performance of our proposed algorithm has a small gap with that of the optimal solution with perfect CSI compared with the other benchmarks.