Two newly observed bands built on a two-quasiparticle configuration in 130Ba have been investigated for the first time with the microscopic projected shell model. The experimental energy spectra and the available electromagnetic transition probabilities are well reproduced. The wobbling character of the higher band is revealed by the angular momentum projected wavefunctions via the K plot and the azimuthal plot. This provides the first strong microscopic evidence for wobbling motion based on a two-quasiparticle configuration in even-even nuclei.