Laser cladding is one of the material additive manufacturing processes used to produce a metallurgically bonded deposition layer. To obtain a high-quality resulting part, a deep understanding of the underlying mechanisms is required. In this article, a mathematical model is developed to simulate the coaxial laser-cladding process with powder injection, which includes laser-substrate, laser-powder, and powder-substrate interactions. The model considers most of the associated phenomena, such as melting, solidification, evaporation, evolution of the free surface, and powder injection. The fluid flow in the melt pool, which is mainly driven by Marangoni shear stress as well as particle impinging, together with the energy balances at the liquid-vapor and the solid-liquid interfaces, are investigated. Powder heating and laser power attenuation due to the powder cloud are incorporated into the model in the calculation of the temperature distribution. The influences of the powder injection on the melt pool shape, penetration, and flow pattern are predicted through the comparison for the cases with powder injection and without powder injection. Dynamic behavior of the melt pool and the formation of the clad are simulated. The effects of the process parameters on the melt pool dimension and peak temperature are further investigated based on the validated model.