This paper investigates the resource allocation problem for the downlink of non-orthogonal multiple access (NOMA) networks. A novel resource allocation method is proposed to deal with the problem of maximizing the system capacity while taking into account user fairness. Since the optimization problem is nonconvex and intractable, we adopt the idea of step-by-step optimization, decomposing it into user pairing, subchannel and power allocation subproblems. First, all users are paired according to their different channel gains. Then, the subchannel allocation is executed by the proposed subchannel selection algorithm (SSA) based on channel priority. Once the subchannel allocation is fixed, to further improve the system capacity, the subchannel power allocation is implemented by the successive convex approximation (SCA) approach where the nonconvex optimization problem is transformed into the approximated convex optimization problem in each iteration. To ensure user fairness, the upper and lower bounds of the power allocation coefficients are derived and combined by introducing the tuning coefficients. The power allocation coefficients are dynamically adjustable by adjusting the tuning coefficients, thus the diversified quality of service (QoS) requirements can be satisfied. Finally, simulation results demonstrate the superiority of the proposed method over the existing methods in terms of system performance, furthermore, a good tradeoff between the system capacity and user fairness can be achieved.