In this paper, we consider the following quaternion tensor equation involving η-Hermicity  where  and  are given quaternion tensors. We derive some necessary and sufficient conditions for the existence of an h-Hermitian solution to this quaternion tensor equation in terms of the Moore-Penrose inverses of the coefficient tensors. We also give an expression of the general h‑Hermitian solution to this quaternion tensor equation when it is solvable. A numerical example is also presented to illustrate the main result of this paper.

quaternion, tensor equation, Moore-Penrose inverse, η-Hermitian solution.