The security in cognitive radio networks (CRNs) has been attracting continuously growing attention, due to the open and dynamic nature of cognitive radio architecture. In this paper, we propose a new relay selection scheme to improve the physical layer security in CRNs. The trusted decode-and-forward (DF) relay is selected to help the source transmission and improve the secrecy rate in the presence of an eavesdropper, and taking into account the primary user quality of service constraint. The performance of the proposed system is analyzed in terms of the achievable secrecy rate and the intercept probability. Asymptotic approximation of the intercept probability at high signal to noise ratios is also derived. The performance comparison of the proposed scheme with the schemes proposed in the literature reveals the superior of the proposed scheme.