This paper presents a novel resource allocation framework for downlink transmissions in MIMO-OFDMA based cognitive radio (CR) networks. In this literature, due to the coexistence of primary and secondary users (SUs) in the same geographical area, the interference induced to the primary users’ (PUs) bands from SUs’ transmissions should be less than the tolerable interference threshold predefined by PU. Hence, the optimal resource allocation strategy is performed subject to the total power constraint in the cognitive base station and the interference power constraint for PUs so that the downlink sum throughput of the CR network can be maximize without causing unacceptable interference. To this aim, two sub-problems are presented and solved theoretically based on convex optimization framework that can be used in the main body of the proposed algorithm. Regarding to the first sub-problem, the resources are distributed among all SUs in a way that just the total power constraint is satisfied. Also, the sum throughput is maximized as the interference power onto the PUs’ bands keeps in a tolerable range in the second sub-problem. So, in order to find the optimum solution, our algorithm consists of three parts. The first two parts include these sub-problems while the last section includes a combination of them. For complexity reduction, two sub-optimal resource allocation algorithms are introduced based on the simplification of main problem constraints. The performance of different approaches is investigated via simulation. Conducted simulation results show that the optimal algorithm achieves better performance in comparison with benchmark algorithms and converges to sub-problem solutions in high and low regimes of interference thresholds.