An exposure apparatus which draws a pattern on a substrate with electron beams. The apparatus includes a substrate stage which supports the substrate, a transfer stage which moves the substrate stage, an electromagnetic actuator which moves the substrate stage relative to the transfer stage, a first measurement system which measures a position of the transfer stage, a second measurement system which measures a position of the substrate stage, a controller which controls the electromagnetic actuator on the basis of measurement results obtained by the first and second measurement systems, a deflector which deflects electron beams with which the substrate is irradiated, and a filter which performs filtering for a measurement result obtained by the second measurement system and supplies the filtered measurement result to the deflector.