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Surface roughness and heat-affected zone (HAZ) are the important features which influence the performance of the laser-drilled products. Understanding the influence of laser process parameters on these responses and identifying the cutting conditions for simultaneous optimization of these responses are a primary requirement in order to improve the laser drilling performance. Nevertheless, no such contribution has been made in the literature during laser drilling of AISI 303 material. The aim of the present work is to optimize the surface roughness (Ra) and HAZ in fibre laser drilling of AISI 303 material using Taguchi-based grey relational analysis (GRA). From the GRA methodology, the recommended optimum combination of process parameters is flushing pressure at 30 Pa, laser power at 2000 W and pulse frequency at 1500 Hz for simultaneous optimization of Ra and HAZ, respectively. From analysis of variance, the pulse frequency is identified as the most influenced process parameters on laser drilling process performance.