The present paper describes the development of Artificial Neural Network (ANN) model and multi-objective optimisation technique to predict and select the optimum machining parameters of the Hole Drilling Electrical Discharge Micromachining (HD-EDMM) process. To predict the performance parameters, ANN model has been developed using back-propagation algorithms. A hybrid method comprising Grey Relational Analysis (GRA) coupled with Principal Component Analysis (PCA) has been used as the optimisation technique for the determination of preferred combination of input parameters of HD-EDMM for maximisation of Material Removal Rate (MRR) and minimisation of Tool Wear Rate (TWR) and hole taper (Ta) simultaneously. Experiments have been planned as per Taguchi L18 orthogonal array and performed under different machining conditions of gap voltage, capacitance of capacitor and revolution per minute of tool electrode. The results indicate that the proposed method is capable of predicting process output and optimising process performance with reasonable accuracy under varied operating conditions of HD-EDMM.