In non-contiguous orthogonal frequency division multiplexing (NC-OFDM)-based interweave cognitive radio networks, the sidelobe power of secondary users (SUs) must be strictly controlled to avoid the interference between the SUs and the primary users (PUs) of the adjacent bands. Similarly, the inherent issue of high peak-to-average power ratio (PAPR) of the OFDM signal is another drawback of the cognitive radio communication system based on the NC-OFDM technology. A few methods are available in the literature to solve either of these problems individually, while in this paper, we propose a new method for the joint minimisation of sidelobe power and PAPR in NC-OFDM-based cognitive radio networks using Zadoff–Chu (ZC) sequence. In this method, the sidelobe power suppression of SUs is benefited by PUs and the PAPR is reduced for SUs. We modelled a new optimisation problem for minimising the sidelobe power with a constraint on the maximum tolerable PAPR and sidelobe power. The proper selection of ZC sequence, which is crucial for minimising both the issues simultaneously, is achieved by solving the proposed optimisation problem. The proposed technique is shown to provide 7 dB and 20 dB reduction in PAPR and sidelobe power, respectively, without causing any signal distortion along with the improvement in bit error rate (BER) performance. © 2016 Informa UK Limited, trading as Taylor & Francis Group.