Nickel-based alloys like Inconel 718 occupy a large share in the aerospace industry because of superior mechanical properties. However, Inconel 718 is categorized as a difficult to machine material. Ultrasonic assisted grinding (UAG), a hybrid grinding process has captured the attention of researchers for grinding of Inconel 718 due its inherent capability in overcoming several problems associated with processing difficult to grind (DTG) materials. Lubrication machining is used for hard to machine materials and minimum quantity lubrication (MQL) is a sustainable method employed to overcome machining problems in such materials. In this context, this work aims to examine UAG of Inconel 718 under different lubrication conditions. Optimization of UAG is necessary in identifying the best parameter combination depending on the process capability of a given machine tool. For this, experimentation using Taguchi L18 orthogonal array parameter design and optimization based on Grey Relational Analysis (GRA) have been performed. The optimization has been performed using grinding forces (tangential force, Ft) and average roughness parameter (Ra) as the output parameters. Additionally, regression models have been developed to enable the prediction of response variables. To determine the factor contribution on output response ANOVA table and S N ratio analysis have been performed on the Grey Relational Grade (GRG). The statistical analysis has revealed feed has the maximum impact on Ra and cutting velocity has the least effect. Similarly, for Ft depth of cut has the maximum effect and cutting velocity has minimum effect. Confirmation experiments reveal that the regression models were able to make accurate predictions under the test conditions. © 2021 Author(s).