In this article, we study a novel intelligent reflecting surface (IRS)-aided cognitive unmanned aerial vehicle (Co-UAV) secure communication network, in which an IRS is exploited to improve the information transmit security. Our goal is to optimize the IRS's phase shifts, the UAV's transmit power and trajectory jointly. Aiming at the non-convex and intractable nature of this optimization objective, we present an effective iterative algorithm by combining alternating optimization (AO) technique and successive convex approximation (SCA) method so as to acquire a local suboptimal solution. Simulation results confirm the proposed algorithm is effective in significantly improving the secondary secrecy performance assisted by IRS subject to the interference temperature limit on the primary user.