Additive Manufacturing (AM) is one of the advanced manufacturing processes that joins materials together in a layer-by-layer addition. This manufacturing technique has a wide range of applications in health care, automotive, and aerospace industries. Even though the AM technique has many advantages over conventional subtractive manufacturing processes, one of the primary limitations of this technique is the quality of surface finish. This study addresses the challenge of predicting surface roughness in AM using machine learning. Surface roughness influences the tribological and thermal properties of these components, making their optimization crucial. Key input variables—layer thickness, extrusion temperature, and print speed—were selected for investigation. A comprehensive dataset was generated from controlled experiments, and several machine learning algorithms were tested to model the relationship between these inputs and surface roughness. The most accurate and reliable among the eleven algorithms is the Random Forest Regressor in terms of the performance characteristics. The major advantage of this algorithm is the ability to solve complex problems with ease, and multi-objective optimization of the AM process makes it the best tool to optimize the surface quality of the printed parts in real time. The current work highlights the importance of Predictive modelling of surface quality in additive manufacturing.