The specific angular momentum of a Kerr black hole must not be larger than its mass in the geometrical units. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. On the other hand, the violation of this bound may suggest the existence of a superspinning object which might be suggested from a string theory argument. In order to investigate observational testability of this bound by using the X-ray energy spectrum of black hole candidates, we calculate the energy spectra from an optically thick and geometrically thin accretion disk of a superspinning object which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. Based on this calculation, we present that the observational confirmation of the Kerr bound is very hard but the violation of it may be detectable if only the continuum X-ray spectrum of the disk is available.