In this paper, we study the resource allocation for a multi-carrier non-orthogonal multiple access (NOMA) system with coordinated direct and relay transmission, where some user equipments (UEs) are directly served by the base station (BS) and other UEs require the help from the relay nodes. In order to fully exploit the degrees of freedom in the systems design, we consider a general set of design parameters, including subcarrier pairing, subcarrier assignment, relay selection and power allocation, to formulate a joint optimization problem. To solve the combinational non-convex problem, we employ the Lagrange dual method and the Hungarian algorithm to obtain an asymptotically optimal solution. Simulation results demonstrate the asymptotic optimality and show that our algorithm significantly outperforms the conventional orthogonal multiple access (OMA) scheme and other existing resource allocation methods.