In this study, new inequalities have been obtained by employing a generalized fractional integral operator which generalizes some fractional integral operators existing in the literature. In the initial step of the study, certain general properties related to Gru¨ ss type inequalities were discussed, followed by establishing a hierarchy among some fractional integral operators already existing in the literature. In the main results section, new lemmas and inequalities of Gru¨ ss type have been obtained using the aforementioned fractional integral operator.