Ultra-hot Jupiters (UHJs) are highly irradiated giant exoplanets with extremely high day-side temperatures, which lead to thermal dissociation of most molecular species. It is expected that the neutral hydrogen atom is one of the main species in the upper atmospheres of UHJs. Neutral hydrogen has been detected in several UHJs by observing their Balmer line absorption. In this work, we report four transit observations of the UHJ WASP-33b, performed with the CARMENES and HARPS-North spectrographs, and the detection of the Hα, Hβ, and Hγ lines in the planetary transmission spectrum. The combined Hα transmission spectrum of the four transits has an absorption depth of 0.99 ± 0.05%, which corresponds to an effective radius of 1.31 ± 0.01 Rp. The strong Hα absorption indicates that the line probes the high-altitude thermosphere. We further fitted the three Balmer lines using the PAWN model, assuming that the atmosphere is hydrodynamic and in local thermodynamic equilibrium. We retrieved a thermosphere temperature 12 200-1000+1300 K and a mass-loss rate Ṁ = 1011.8-0.5+0.6 g s-1. The retrieved high mass-loss rate is compatible with the "Balmer-driven" atmospheric escape scenario, in which the stellar Balmer continua radiation in the near-ultraviolet is substantially absorbed by excited hydrogen atoms in the planetary thermosphere.