This paper considers the problem of designing the reliable LQG controller of discrete-time systems with sensor outages. A sequential gain computing algorithm is formulated for LQG optimal control (LQGOC) by using the conventional sequential measurement update equations. With this new gain computing scheme, the reliable control design problem in case of sensor outages is reviewed and solved by using a special case of this new result. In addition, the bounds of gain margins for the reliable Kalman gain are also given. A numerical example is given to show the effectiveness of the obtained results.