Abstract: Laser-directed energy deposition (L-DED), as a coaxial powder feeding metal additive manufacturing process, has a broad application prospect in the fields such as aerospace and transportation for its' advantages of high deposition rate and fabrication of large parts. However, the L-DED suffers from process defects in the resolution of metal part size and shape, such as significant size deviation and surface unevenness, which requires high efficiency and accurate numerical model to predict the shape and size of the cladding track. In this work, we proposed a high-fidelity multi-physics numerical model that considers the interaction between powders, laser beam, and melt pool. In this model, the laser beam is modeled as a Gauss surface heat source, a Lagrangian particle-based model is used for the powders-laser beam interaction, and then the Lagrangian particle-based model is integrated to finite volume method and volume of fluid to simulate the interaction between powders and melt pool and the corresponding melting and solidification process. The proposed model is validated by the experimental data of single-track TC17 alloy fabricated using L-DED. Based on the validated numerical model, a set of single tracks with different combinations of process parameters are predicted, followed by an in-depth analysis of process parameters' effect on the sizes and shapes of the cladding tracks and the corresponding underlying physical mechanism. It is identified that the process parameters dependent temperature distribution of the injected powders and the ratio of energy absorbed by powders to that by the substrate play an essential role in the velocity field of the melt pool and the size and shape of the cladding track. We expect that the proposed numerical model is a powerful tool to aid the process parameters optimization for the L-DED additive manufacturing process. At the same time, the results of this study can provide theoretical guidance on the shape and size resolution control of the fabricated parts.