Molecular-theory-based dynamic tensor models of liquid crystals typically contain high-order moment tensors, which are necessarily expressed by the order parameter tensors to close the system. Such closure approximation can be given either by some simple formula, which largely ignore the mathematical structures of the original dynamics, or by the maximum entropy state, which better maintains the structures but computationally expensive. The quasi-entropy, a class of elementary functions, has been proposed to substitute the entropy term given by the maximum entropy state in the free energy. It has been shown that it keeps the significant mathematical properties of the original entropy and captures the underlying physics in representative cases. We further propose a novel approach of closure approximation by the quasi-entropy, illustrated by a tensor model of rod-like molecules, that is capable of keeping the essential structures in the dynamics and is easy to implement.