［Purposes］ The goal is to study the relationships between L?wner partial orders A ≥ B and A > B and their Moore Penrose inverses. ［Methods］ By using the eigenvalues, range, Moore-Penrose inverse of tensor, the L?wner partial orders A ≥ B and A > B are studied. ［Findings］ Some basic properties and equivalent conditions of partial orders A ≥ B and A > B are obtained. ［Conclusions］ The sufficient and necessary conditions of L?wner partial order A ≥ B and A > B show that the properties of matrix L?wner partial ordering can be generalized to tensors.