Cognitive radio (CR) is an effective solution to increase the spectral efficiency (SE) of wireless communications by allowing the secondary users (SUs) to share the spectrum with primary users (PUs). On the other hand, intelligent reflecting surface (IRS) is a promising approach to enhance the energy efficiency (EE) of wireless communication systems through passively reconfiguring the channel environments. In this paper, we propose an IRS enhanced downlink multiple-input single-output (MISO) CR systems to improve both SE and EE, where a single SU coexists with a primary network with multiple primary user receivers (PU-RXs). Specifically, for the MISO-CR system, we maximize the achievable rate of SU subject to a total power constraint on an SU transmitter (SU-TX) and an interference temperature (IT) constraint on PU-RXs, by jointly optimizing the beamforming vector at SU-TX and the phase shifts at the IRS. Furthermore, both perfect channel state information (CSI) and imperfect CSI are considered in the optimization. Numerical results demonstrate that the IRS can significantly improve the achievable rate of SU-RX under both the perfect and imperfect CSI conditions.