Abstract: The combination of Terahertz (THz) frequency band and Non-Orthogonal Multiple Access (NOMA) technology has outstanding advantages in realizing large-scale connection and ultra-high speed communication. However, there are few researches on resource allocation of downlink THz-NOMA system, and the existing resource allocation schemes have disadvantages of high algorithm complexity and low system performance. In order to obtain a resource allocation scheme that is balanced in both complexity and performance, this paper studies the resource allocation problem of downlink THz-NOMA system with the optimization goal of maximizing energy efficiency. Firstly, in order to reduce the complexity of matching between users and subchannels, the subchannel allocation problem is equivalent to the Two-Side Match (TSM) problem, and a low-complexity TSM subchannel allocation algorithm is proposed. Secondly, in view of the non-convexity of inter-channel power allocation problem, this paper transforms the non-convex function into the difference of two convex functions, and proposes an inter-channel power allocation algorithm based on difference convex programming. The solution of inter-channel power allocation problem is obtained by solving the convex subproblem iteratively. For user power allocation in subchannels, a closed form solution of optimal user power allocation in subchannels is derived. Simulation results show that the proposed subchannel matching algorithm is less complex than the switching matching algorithm, and the proposed power allocation algorithm can achieve higher system energy efficiency than the traditional power allocation algorithm.