This paper investigates the joint subcarrier and power allocation problem for the downlink of a multi-carrier non-orthogonal multiple access (MC-NOMA) system. A novel three-step resource allocation framework is designed to deal with the sum rate maximization problem. In Step 1, we relax the problem by assuming each of the users can use all subcarriers simultaneously. With this assumption, we prove the convexity of the resultant power control problem and solve it via convex programming tools to get a power vector for each user; In Step 2, we allocate subcarriers to users by a heuristic greedy manner with the obtained power vectors in Step 1; In Step 3, the proposed power control schemes used in Step 1 are applied once more to further improve the system performance with the obtained sub-carrier assignment of Step 2. To solve the maximization problem with fixed subcarrier assignments in both Step 1 and Step 3, a centralized power allocation method based on projected gradient descent algorithm and two distributed power control strategies based respectively on pseudo-gradient algorithm and iterative waterfilling algorithm are investigated. Numerical results show that our proposed three-step resource allocation algorithm could achieve comparable sum rate performance to the existing near-optimal solution with much lower computational complexity and outperforms power controlled OMA scheme. Besides, a tradeoff between user fairness and sum rate performance can be achieved via applying different user power constraint strategies in the proposed algorithm.