This article reports an investigation on the impacts of pivot locations and pitching angular offsets on the two-dimensional flapping elliptic airfoil’s time-averaged and transient aerodynamic force coefficients. The study is carried out using ANSYS FLUENT solver and water tunnel experiments. Three different pivot point locations and pitch angular offsets are considered while keeping the flapping frequency fixed at 0.32, pitching amplitude at 30° and Reynolds number at 5000. The flapping airfoil generates a non-zero time-averaged lift for a non-zero pitch angular offset due to asymmetry kinematics in the downstroke and upstroke of a flapping cycle at all pivot locations. Furthermore, the time-averaged lift performance of the flapping airfoil is substantially improved at every pivot point locations for increased pitch angular offset. However, the time-averaged thrust generally deteriorates with the pitch angular offset, except at small pitch angular offset values. We have further identified the optimum pivot location and pitch angular offset for superior aerodynamic performances at the considered parametric range of investigation.