Model based approaches show a lot of advantages for fault detection and condition monitoring. Particularly, it is true in employing reduced order models for real-time parameter identification and output prediction of gas turbines. Many algorithms have been developed, but most of them focus on one-step-ahead prediction models and involve complex computation. These algorithms are not acceptable for long-term prediction and real-time condition monitoring. In this paper, an improved gradient method (Dynamic Gradient Descent) is proposed. The idea is to take account of the dependency of prediction errors and calculate the gradient information recursively. Not only low computation expense is achieved, but the non-Gaussian errors can also be overcome when this approach is applied to estimate parameters of a reduced order gas turbine model and to improve longterm prediction.