A new attitude estimation method for a spacecraft is derived. This method employs a receding-horizon strategy to use a time window and constraint. A conventional constrained filter, the receding-horizon nonlinear Kalman filter (RNKF), propagates the state value in the prediction step, and minimizes the cost function with a constraint in the filtering step. It is desirable for the optimization to be a quadratic programming (QP) problem, whose constraint is linear, in terms of computational complexity. If the RNKF is applied to the attitude estimation problem, the appropriate attitude representation is the quaternion, which has no singular point, in the prediction step. However, the quaternion does not define a QP problem in the filtering step because the quaternion needs to satisfy a single constraint of a unit norm. Therefore, this paper proposes the receding-horizon unscented Kalman filter (RUKF), which is an improvement of the RNKF, to deal with appropriate attitude representation in each step. In the RUKF, each attitude of a time window is represented by generalized Rodrigues parameters (GRPs) in the filtering step employing the successive unscented transformation. The GRPs is an attitude representation with no constraint. Simulation revealed that the RUKF is more accurate than the extended Kalman filter.