This paper studies the output-feedback LQG control of a two-player system with one-step communication delay. A novel information pattern is considered and a new controller structure is introduced. The proposed controller consists of two parts: the first part is based on estimated system state; the second part is based on current local measurement output. The form of the optimal controller is established using the method of independence decomposition. A necessary condition is established to construct the optimal controller gains. Two iterative algorithms are used to find the optimal gains numerically. Finally, the effectiveness of the theoretical results is illustrated through a numerical example.