An electron beam exposure apparatus which exposes a substrate with a predetermined pattern using one or a plurality of electron beams. The apparatus includes a substrate stage on which a substrate is mounted, a transfer stage which drives the substrate stage on an X-Y plane, an electromagnetic actuator which drives the substrate stage in a rotation direction about a Z-axis with respect to the transfer stage, and a measuring system which measures a position of the substrate stage in the rotation direction about the Z-axis using a measuring beam along a direction perpendicular to the plurality of electron beams.