To solve the slow convergence speed and low estimation accuracy of the extended Kalman filter (EKF) for the complex nonlinear state estimation, the square root cubature Kalman filter (SRCKF) is introduced in the study. In the SRCKF algorithm, the cubature rule based numerical integration method is directly used to calculate the mean and covariance of the nonlinear random function. The algorithm is implemented only using the functional evaluation and is derivative-free so the computational complex is decreased. And the SRCKF propagates the square root of the covariance so that it guarantees the symmetry and positive semi-definiteness of the covariance matrix and improves numerical stability and numerical accuracy. The algorithm is applied to state estimation for reentry ballistic target with unknown ballistic coefficient. The simulation results indicate that the state error in the SRCKF is largely decreased and its estimation accuracy is improved. Moreover, the run speed of SRCKF is faster.