Electronic structures of the quantum critical superconductor beta-YbAlB4 and its polymorph alpha-YbAlB4 are investigated by using bulk-sensitive hard x-ray photoemission spectroscopy. From the Yb 3d core level spectra, the values of the Yb valence are estimated to be similar to 2.73 and similar to 2.75 for alpha- and beta-YbAlB4, respectively, thus providing clear evidence for valence fluctuations. The valence band spectra of these compounds also show Yb2+ peaks at the Fermi level. These observations establish an unambiguous case of a strong mixed valence at quantum criticality for the first time among heavy fermion systems, calling for a novel scheme for a quantum critical model beyond the conventional Doniach picture in beta-YbAlB4.