In this paper, a downlink security-aware resource allocation problem with delay constraint via spectrum sensing is modeled as a mixed integer non-linear problem for non-orthogonal multiple access-based cognitive radio network. The security-aware resource allocation is subject to constraints in required delay for each secondary user, maximum number of accessed secondary users at each subchannel, total interference power threshold introduced to primary users, and total power consumption at secondary BS. The security-aware resource allocation is based on channel state information at the physical layer and queue state information at the link layer. According to the queue buffer occupancy, a probability upper bound of exceeding the maximum packet delay based on M/D/1 queuing model is analyzed in terms of a required minimum secrecy transmission rate. Then, a secondary user scheduling problem and a power allocation problem are solved, separately. Finally, the secondary user scheduling problem is solved via greedy algorithm, and a power allocation algorithm is proposed by successive convex approximation method. The simulation results demonstrate that the performance of proposed algorithms can be improved significantly.