The effect of various wire electrical discharge machining process parameters such as pulse on time, pulse off time, pulse current and the wire drum speed on machined surface quality characteristics such as surface roughness and kerf width has been discussed. The experiments were carried out with L₂₇ orthogonal array on hybrid metal matrix composite prepared by inert gas–assisted electromagnetic stir casting process using particulates 7.5% Al₂O₃ and 7.5% SiC each in Al7075 alloy. Taguchi-based grey relational analysis, a multi-response optimization technique, was used to find the optimal process parameter setting for the best quality machined characteristics. Results of analysis of variance showed that the order of significance was pulse on time, pulse current, pulse off time and the wire drum speed contributing 50.02%, 39.50%, 4.58% and 2.75%, respectively, while machining the hybrid composite. Confirmation test was carried out at selected optimal parameter setting, which showed improvement in grey relational grade, thus confirming the robustness of grey relational analysis.