The use of laser cladding technology to prepare coatings of AlCoCrFeNi high-entropy alloy holds enormous potential for application. However, the cladding quality will have a considerable effect on the properties of the coatings. In this study, considering the complex coupling relationship between cladding quality and the process parameters, an orthogonal experimental design was employed, with laser power, scanning speed, and powder feed rate as correlation factor variables, and microhardness, dilution rate, and aspect ratio as characteristic variables. The experimental data underwent gray correlation analysis to determine the effect of various process parameters on the quality of cladding. Then, the NSGA-II algorithm was used to establish a multi-objective optimization model of process parameters. Finally, the ANSYS Workbench simulation model was employed to conduct numerical simulations on a group of optimized process parameters and analyze the change rule of the temperature field. The results demonstrate that the laser cladding coating of AlCoCrFeNi high-entropy alloy with the single pass is of high quality within the determined orthogonal experimental parameters. The powder feed rate exerts the most significant influence on microhardness, while laser power has the greatest impact on dilution rate, and scanning speed predominantly affects aspect ratio. The designed third-order polynomial nonlinear regression model exhibits a high fitting accuracy, and the NSGA-II algorithm can be used for multi-objective optimization to obtain the Pareto front solution set. The numerical simulation results demonstrate that the temperature field of AlCoCrFeNi high-entropy alloy laser cladding exhibits a “comet tail” phenomenon, where the highest temperature of the molten pool is close to 3000 °C. The temperature variations in the molten pool align with the features of laser cladding technology. This study lays the groundwork for the widespread application of laser cladding AlCoCrFeNi high-entropy alloy in surface engineering, additive manufacturing, and remanufacturing. Researchers and engineering practitioners can utilize the findings from this research to judiciously manage processing parameters based on the results of gray correlation analysis. Furthermore, the outcomes of multi-objective optimization can assist in the selection of appropriate process parameters aligned with specific application requirements. Additionally, the methodological approach adopted in this study offers valuable insights applicable to the exploration of various materials and diverse additive manufacturing techniques.