In this research, we propose a design method for a nonlinear optimal attitude control system that combines the systems of a single-gimbal control moment gyro (SGCMG) and a satellite that were conventionally designed separately. For this purpose, we designed a state-dependent linear representation model integrating satellite dynamics and SGCMG dynamics using a State-Dependent Riccati Equation (SDRE) controller. In the proposed method, it is possible to design the gimbal angular velocity as input without solving the inverse kinematics in the pyramid-type SGCMG. Therefore, it is possible to avoid the singularity of SGCMG by designing the weighting function matrices considering the relationship between the maneuvering axis and SGCMG steering. A numerical simulation shows that it is possible to achieve a high-speed attitude maneuver of the satellite by optimal attitude control considering singularity avoidance by the proposed method. In addition, usefulness of proposed law is shown in comparison with the GSR Inverse steering logic for the agile attitude maneuver.