Targets tracking is one of the most important issues in various fields, such as active defense, medicine, and so on. Although The Kalman filter is one of the useful tools for tracking targets, its performance may degrade when the target is maneuvering. Also, in many studies in the field of maneuvering targets tracking , the dynamic model of the target is assumed to be linear. In this dissertation, a two-dimensional and nonlinear curvilinear model is used to increase the tracking accuracy, in which the vector of acceleration and turn rate are cosidered to be either deterministic unknowns or random processes. As the acceleration vector and the turn rate in the dynamic model are unknown and also to increase tracking accuracy, different methods of estimating the target acceleration vector are investigated and then a new method is proposed to estimate the stare vector, using a two-stage Kalman filter. After that, in another proposed method, by adding the acceleration vector and the turn rate to the state vector, the target dynamic model is recasted and the new state vector is estimated using a nonlinear filter. Since, the covariance matrices of the system and measurement noises and acceleration (in the case of randomness) are unknown to the tracking system, in practice, they are also estimated along with the state estimation. Finally, the proposed method are compared with the existing methods for maneuvering target tracking with curvilinear dynamic model through simulation. Key Words : Target Tracking , Target Maneuver , Kalman Filter , Dynamic Model, Two-Stage Kalman Filter.