Gradient Boosting is a machine learning algorithm that combines several simple parameter functions that aim to predict a fairly accurate information from existing data. In contrast to statistical methods in general, this Gradient boosting provides interpretable information, while requiring little data preprocessing and tuning of parameters. Boosting Gradient can be applied to classify or regress data, complex interaction is modeled simply and minimizes loss of information while in predictor management, so this algorithm is good enough to be used for modeling the cost of insurance loss. This paper presents the GB theory and its application to the problem of predicting '' at-fault '' accidents on auto loss costs using data from Canadian insurance companies. The predictive accuracy of the model is compared to the conventional Generalized Linear Model (GLM) approach.Gradient Boosting is a machine learning algorithm that combines several simple parameter functions that aim to predict a fairly accurate information from existing data. In contrast to statistical methods in general, this Gradient boosting provides interpretable information, while requiring little data preprocessing and tuning of parameters. Boosting Gradient can be applied to classify or regress data, complex interaction is modeled simply and minimizes loss of information while in predictor management, so this algorithm is good enough to be used for modeling the cost of insurance loss. This paper presents the GB theory and its application to the problem of predicting '' at-fault '' accidents on auto loss costs using data from Canadian insurance companies. The predictive accuracy of the model is compared to the conventional Generalized Linear Model (GLM) approach.