In this letter, the secrecy performance in cognitive radio networks (CRNs) over fluctuating two-ray (FTR) channels, which is used to model the milimeter wave channel, is investigated in terms of the secrecy outage probability (SOP). Specifically, we consider the case where a source (S) transmits confidential messages to a destination (D), and an eavesdropper wants to wiretap the information from S to D. In a CRN framework, we assume that the primary user shares its spectrum with S, where S adopts the underlay strategy to control its transmit power without impairing the quality of service of the primary user. After some mathematical manipulations, an exact analytical expression for the SOP is derived. In order to get physical and technical insights into the effect of the channel parameters on the SOP, we derive an asymptotic formula for the SOP in the high signal-to-noise ratio region of the S-D link. We finally show some selected Monte-Carlo simulation results to validate the correctness of our derived analytical expressions.