The escaping atmospheres of hydrogen driven by stellar X-ray and extreme ultraviolet (XUV) have been detected around some exoplanets by the excess absorption of Ly alpha in the far-ultraviolet band. In the optical band the excess absorption of H alpha is also found by ground-based instruments. However, it is not certain if the escape of the atmosphere driven by XUV can result in such absorption. Here we present the XUV-driven hydrodynamic simulation coupled with the calculation of detailed level population and the process of radiative transfer for WASP-121b. Our fiducial model predicts a mass-loss rate of similar to 1.28 x 10(12) g s(-1) for WASP-121b. Due to the high temperature and Ly alpha intensity predicted by the fiducial model, many hydrogen atoms are populated into the first excited state. As a consequence, the transmission spectrum of H alpha simulated by our model is broadly consistent with the observation. Compared with the absorption of H alpha at different observation times, the stellar XUV emission varies in the range of 0.5-1.5 times fiducial value, which may reflect the variation of the stellar activity. Finally, we find that the supersonic regions of the planetary wind contribute a prominent portion to the absorption of H alpha by comparing the equivalent width of H alpha, which hints that a transonic outflow of the upper atmosphere driven by XUV irradiation of the host star can be detected by a ground-based telescope and that H alpha can be a good indicator of escaping atmosphere.