In order to solve the problem of the declining tracking accuracy for O-E theodolite caused by maneuvering target model inaccurate, the single hidden layer feedforward networks(SLFNs) model was built for maneuvering target, then an dual extended Kalman filter(DEKF) on-axis tracking control method was proposed. The key state parameters of the mathematical model were estimated by the dual extended Kalman filter(DEKF). In the simulation and experiments, the predicted target velocity error is about 0.070 9(°)/s at the peak of velocity and the tracking accuracy is 2.42′ when tracking the equivalent sine object of 83.33°sin0.6t, the tracking accuracy reaches 2.96′ when tracking the optical dynamic target with 4.5 s rotation period. Tracking results show that SLFNs mode is matched for maneuvering target, DEKF can fast track and estimate the state parameters. As compared with other control methods, the proposed method has higher accuracy and improves the system tracking precision significantly.