Geometric moments are useful in pattern recognition, and several optical methods have been proposed for their calculation. In this paper, we present a new hybrid optical/digital processor that computes the geometric moments using the recently introduced Hartley transform (HT). This transform has the attractive property of being real when the signal is real. We prove an important result, that all geometric moments of an image can be computed recursively from the various partial derivatives (near origin) of the HT intensity. An analytical example is provided to illustrate the proposed method.