Accurate trajectory prediction is crucial for autonomous driving, yet uncertainty in agent behavior and perception noise makes it inherently challenging. While multi-modal trajectory prediction models generate multiple plausible future paths with associated probabilities, effectively quantifying uncertainty remains an open problem. In this work, we propose a novel multi-modal trajectory prediction approach based on evidential deep learning that estimates both positional and mode probability uncertainty in real time. Our approach leverages a Normal Inverse Gamma distribution for positional uncertainty and a Dirichlet distribution for mode uncertainty. Unlike sampling-based methods, it infers both types of uncertainty in a single forward pass, significantly improving efficiency. Additionally, we experimented with uncertainty-driven importance sampling to improve training efficiency by prioritizing underrepresented high-uncertainty samples over redundant ones. We perform extensive evaluations of our method on the Argoverse 1 and Argoverse 2 datasets, demonstrating that it provides reliable uncertainty estimates while maintaining high trajectory prediction accuracy.