In this paper, we investigate a non-orthogonal multiple access (NOMA)-based underlay multi-channel cognitive device-to-device (D2D) communications and efficiently exploit a resource management scheme for the investigated model. A two-stage solution is used in which sub-channels (SCs) and powers are jointly assigned to the D2Ds and transmitters, respectively, employing a convex optimization method to achieve the optimal parameters. We show that throughput of the D2D users can be maximized by the proposed strategy, subject to controlling total transmission power, interference power, and minimum rate requirements. We study the performance of the network by increasing the number of PUs and SCs. Moreover, minimum rate requirement and maximum allowed interference at the PUs versus sum rate of the SU transceivers is investigated. The simulation results present insights about the impact of the optimal power and SC allocations.