The unknown inputs in practical engineering applications will lead to the decline of the accuracy of the classical nonlinear filter state estimation and even the divergence of the filter. In order to address this problem, in this paper, an extended square-root cubature Kalman filter (ESRCKF) algorithm according to the minimum variance unbiased estimation (MVUE) criterion is proposed. Firstly, the one-step predicted value of state is modified by combining with the unknown input estimated value at the previous time to obtain the predicted value of state under the condition of unknown input. Secondly, the unbiased estimation of the unknown input at the current time is obtained by using innovation and weighted least squares (WLS) method. Finally, the minimum variance unbiased estimation of the system state is obtained by minimizing the trace of the covariance matrix, while using the Lagrange multiplier method and the Schur complement lemma. Simulation results demonstrate that compared with the existing nonlinear filtering algorithms, ESRCKF algorithm improves the accuracy of state estimation when dealing with nonlinear systems with unknown inputs, and can simultaneously achieve the optimal estimation of system state and unknown inputs, which validates the effectiveness of the algorithm.