The main objective of this research paper is to build an appropriate mathematical model that helps in forecasting third party claim amount for different categories of vehicles based on the chosen characteristics of the data. In actuarial research, predicting the insurance claim amount for different vehicle categories is a challenging task, and minimal empirical research studies were done to forecast the claims. In the present study, the annual time series historical data were collected for a period of 34 years. We had built the machine learning predictive models to modeling the claim amount with different categories of vehicles effectively. In this context, we exhibited the feasibility of using a statistical machine learning approach such as Linear regression Model, the Exponential Smoothing Model, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and hybrid ARIMA-ANN models to predict the various categories of vehicles claim amount. The data were analyzed, compared, and the empirical analysis showed that Artificial Neural Network is a better predictive model among the other time series models based on performance evaluation metrics RMSE and MAPE with lesser variance. Therefore, the machine learning approach for forecasting third party claim amounts will help the Insurance Companies in India to provide a better predictive model, which ensures better claims settlement and management for different categories of vehicles.