Echolocating bats can identify three-dimensional objects exclusively through the analysis of acoustic echoes of their ultrasonic emissions. However, objects of the same structure can differ in size, and the auditory system must achieve a size-invariant, normalized object representation for reliable object recognition. This study describes both the behavioral classification and the cortical neural representation of echoes of complex virtual objects that vary in object size. In a phantom-target playback experiment, it is shown that the bat Phyllostomus discolor spontaneously classifies most scaled versions of objects according to trained standards. This psychophysical performance is reflected in the electrophysiological responses of a population of cortical units that showed an object-size invariant response (14/109 units, 13%). These units respond preferentially to echoes from objects in which echo duration (encoding object depth) and echo amplitude (encoding object surface area) co-varies in a meaningful manner. These results indicate that at the level of the bat's auditory cortex, an object-oriented rather than a stimulus-parameter-oriented representation of echoes is achieved.