The quality assessment and prediction becomes one of the most critical requirements for improving reliability, efficiency and safety of laser welding. Accurate and efficient model to perform non-destructive quality estimation is an essential part of this assessment. This paper presents a structured and comprehensive approach developed to design an effective artificial neural network based model for weld bead geometry prediction and control in laser welding of galvanized steel in butt joint configurations. The proposed approach examines laser welding parameters and conditions known to have an influence on geometric characteristics of the welds and builds a weld quality prediction model step by step. The modelling procedure begins by examining, through structured experimental investigations and exhaustive 3D modelling and simulation efforts, the direct and the interaction effects of laser welding parameters such as laser power, welding speed, fibre diameter and gap, on the weld bead geometry (i.e. depth of penetration and bead width). Using these results and various statistical tools, various neural network based prediction models are developed and evaluated. The results demonstrate that the proposed approach can effectively lead to a consistent model able to accurately and reliably provide an appropriate prediction of weld bead geometry under variable welding conditions.