Tweedie models can be used to handle non-negative continuous data with a probability mass at zero. There have been wide applications in natural science, healthcare research, actuarial science and other fields. The performance of existing Tweedie models can be limited by today’s complex data problems with challenging characteristics such as high-dimensionality, nonlinear effects, high-order interactions. Motivated by these challenges, we propose a kernel Tweedie model with integrated variable selection. The non parametric nature of the the proposed method along with the abundance of available kernel functions provides much needed modeling flexibility and capability. The resulting sparsity due to the variable selection also improves the interpretability and the prediction accuracy. We perform extensive simulation studies to justify the prediction and variable selection accuracy of our method, and demonstrate the applications in ratemaking and loss-reserving in general insurance. The model is implemented in an efficient and user-friendly R package.