Laser wire-feed metal additive manufacturing (LWAM) is an innovative technology that shows many advantages compared with traditional manufacturing approaches. Despite these advantages, its industrial adoption is limited by complex parameter management and inconsistent process quality. To address these issues and improve geometric accuracy, this study explores how process parameters influence bead geometry. We conducted a parameter study varying laser power, wire feed rate, traverse speed, and welding angle. Using a full factorial design with a central composite design methodology, we assessed bead height and width. This allowed us to develop a model to estimate ideal process parameters. The findings offer a detailed analysis of parameter interactions and their effects on bead geometry, aiming to enhance geometric accuracy and process stability in LWAM. Moreover, we have evaluated the proposed process parameters from our developed model, which showed a significant enhancement to the overall quality. This was validated via printing a single layer and multi-layer structures. The quality of the final predicted sample using the proposed method was improved by 40% compared to the best sample produced for the Design of Experiment trials.