A new set of attitude parameters that minimize the eigenangle between a body-fixed frame and a target reference frame was developed for application to rapid attitude maneuver of a spacecraft. The target reference frame is defined by using the pointing vector from the spacecraft to the target. Attitude kinematics based on the new set of attitude parameters is subsequently derived. To accomplish fast attitude maneuver, a cascade-saturation controller is then designed based on the proposed attitude parameters. The constraints of slew rate and control torque are considered in the proposed cascade-saturation controller. The stability of the resulting closed-loop system is proved by the Lyapunov theory. Simulation results verify that the proposed parameters are well-suited for spacecraft rapid target acquisition and tracking control.