Laser drilling is a well-established manufacturing process utilised to produce holes in various aeroengine components. This research presents an experimental investigation on the effects of laser drilling process parameters on productivity (material removal rate), hole quality (hole taper) and drilling cost. Single-pulse drilling was employed to drill a thin-walled Inconel 718 superalloy plate of 1 mm thickness using pulsed Nd:YAG laser. The experiments were designed using Box-Behnken statistical approach to investigate the impacts of pulse energy, pulse duration, gas pressure and gas flow rate on the selected responses. Multi-objective optimisation was performed using response surface methodology (RSM) based grey rational analysis (GRA) to identify optimal drilling conditions aiming to maximise the MRR and minimise hole taper and drilling cost. The optimal combination of drilling parameters was found as pulse energy of 20 J, pulse duration of 6 ms, gas pressure of 100 psi and gas flow rate of 40 mm3/s. A detailed cost analysis identified labour cost, gas consumption and machine costs as the major cost elements of the laser drilling process.