The Generalized Extreme Value (GEV) distribution is the most commonly used distribution for analyzing extreme values. However, the existing GEV models are based on the assumption that the extreme values are independent, which is sometimes not the case in real data analysis. This thesis aims to overcome this issue by bringing forward a new GEV model that considers the correlation between two successive extreme values. The proposed model can be applied to both independent and dependent extreme values. The point estimation and interval estimation methods for the model parameters are introduced. Simulation studies describe the estimation performance under different combinations of parameters and show that the proposed methods have better performance than the traditional GEV model. Moreover, a study of the Average Run Length (ARL) for the GEV model is conducted through simulation. In the end, two real data analyses are included to illustrate the application of our methodology.