We present a theoretical analysis for the Goos-Hänchen and Imbert-Fedorov shifts experienced by an X-wave upon reflection from a dielectric interface. We show that the temporal chirp, as well as the bandwidth of the X-wave, directly affect the spatial shifts in a way that can be experimentally observed, while the angular shifts do not depend on the spectral features of the X-wave. A dependence of the spatial shifts on the spatial structure of the X-wave is also discussed.