This paper presents an attitude control method for underactuated spacecraft with unmeasurable angular velocity. Based on the second-order sliding mode observer, unknown angular velocity is accurately estimated. The \(w - z\) parameter model is selected and the average kinematics model of the underactuated spacecraft is constructed by means of the average theory On this basis, the exponential stable control law is designed to make the underactuated spacecraft attitude stable, and the global stability of the closed-loop system is proved. Finally, the effectiveness of the controller is verified by numerical simulations.