This paper reports parametric optimisation of air plasma arc cutting (PAC) of structural steel St.52-3, which is widely used in bridge construction and ship building. Response variables considered are material removal rate, a surface roughness (Rz5-mean height of profile) as well as a size of heat affected zone (HAZ) which are critical for corresponding fatigue life. Screening experiment showed pressure, current, arc voltage and speed as factors having an influence on responses of interest. The experimental runs were planned by using Box-Behnken response surface design, and the grey-based fuzzy algorithm was employed to predict the optimal process parameter setting combination. The confirmation test conducted shows an improvement in grey-fuzzy relational grade by about 19%. This highlights the usefulness of grey-fuzzy algorithm as a multi-objective optimiser for plasma arc cutting. The effect of process parameters on performance characteristics has also been discussed resulting in better understanding of the plasma arc cutting process. [Submitted 29 July 2017; Accepted 15 April 2018]