In terms of the uncertainty measurement and the constraint on the attitude quaternion, this paper proposes a quaternion constrained cubature Kalman filter based on uncertain measurements (UCCKF) for the spacecraft attitude estimation system. The proposed filter algorithm overcomes the limitation of the quaternion-constrained cubature Kalman filter. An independent Bernoulli random process is introduced to describe the measurement uncertainty, and the three degree spherical radial cubature rule is adopted to computer the posterior mean and covariance of the system state. To deal with quaternion normalization problem, the two-step projection theory is applied to solve the quaternion constraint. Simulation results show that, compared with constrained cubature Kalman filter and unscented mixture filter, the proposed UCCKF can help to implement the better convergence and higher estimation accuracy in the case of measurement uncertainty. This illustrates that the proposed algorithm is effective and feasible for the nonlinear attitude estimation system.