We investigated the quasi-periodic pulsation (QPP) in Ly-α, X-ray and extremeultraviolet (EUV) emissions during two solar flares, i.e., an X-class (SOL2012-01-27T) and a C-class (SOL2016-02-08T). The full-disk Ly-α and X-Ray flux during these solar flares were recorded by the EUV Sensor and X-Ray Sensor on board the Geostationary Operational Environmental Satellite. The flare regions were located from the EUV images measured by the Atmospheric Imaging Assembly. The QPP could be identified as a series of regular and periodic peaks in the light curves, and its quasi-periodicity was determined from the global wavelet and Fourier power spectra. A quasi-periodicity at about 3 minutes is detected during the impulsive phase of the X-class flare, which could be explained as the acoustic wave in the chromosphere (e.g., Milligan et al. 2017). Interestingly, a quasi-periodicity at roughly 1 minute is discovered during the entire evolutionary phases of solar flares, including the precursor, impulsive, and gradual phases. This is the first report of 1-minute QPP in the Ly-α emission during solar flares, in particular during the flare precursor. It may be interpreted as a self-oscillatory regime of the magnetic reconnection, such as magnetic dripping.