The traditional tracking algorithms for continuous-time nonlinear dynamic system face two problems: linearization and discretization, this greatly degrades the tracking performance, especially for the cases of stronger dynamic nonlinearity or longer revisit time. In this paper, a novel algorithm called Numerical integration based Kalman filter (NIKF) which can avoid the linearization and discretization steps is presented. The NIKF use numerical integration to predict the state and covariance instead of the series expansion based methods. By using a simple fourth-order Runge-Kutta numerical integration, the prediction error is reduced to a considerably lower level. An example of re-entry target tracking indicates that the algorithm significantly outperforms the traditional algorithms (e.g., an Extended Kalman filter (EKF)) in the tracking accuracy and filtering robustness.