It is well known that the high peak-to-average power ratio (PAPR) and large spectrum side lobe power are two primary disadvantages at the transmitter in non-contiguous orthogonal frequency division multiplexing (NC-OFDM) based cognitive radio (CR) systems. In this paper, we propose a novel signal cancellation (SC) method for joint PAPR reduction and side lobe suppression in NC-OFDM based CR systems. The key thought of the proposed strategy is to rapidly expand some part of constellation points on the secondary user (SU) subcarriers and include a few signal-cancellation symbols on the primary user (PU) subcarriers, to create the appropriate cancellation signal for joint PAPR reduction and side lobe suppression. At that point, the SC method formulates the problem of the joint PAPR reduction and side lobe suppression as a quadratic ally constrained quadratic program (QCQP) to acquire its optimal cancellation signal. In addition, we also propose a suboptimal SC (Sub-SC) strategy to efficiently solve the QCQP optimization problem with low computational complexity. Simulation results show that the proposed SC method and Sub-SC technique can provide both significant PAPR reduction and side lobe suppression performances.