Quasi-periodic pulsations (QPPs), which usually appear as temporal pulsations of the total flux, are frequently detected in the light curves of solar/stellar flares. In this study, we present the investigation of non-stationary QPPs with multiple periods during the impulsive phase of a powerful flare on 2017 September 06, which were simultaneously measured by the Large-Yield RAdiometer (LYRA) and the Hard X-ray Modulation Telescope (Insight-HXMT), as well as the ground-based BLENSW. The multiple periods, detected by applying a wavelet transform and Lomb-Scargle periodogram to the detrended light curves, are found to be ∼20−55 s in the Lyα and mid-ultraviolet Balmer continuum emissions during the flare impulsive phase. Similar QPPs with multiple periods are also found in the hard X-ray emission and low-frequency radio emission. Our observations suggest that the flare QPPs could be related to nonthermal electrons accelerated by the repeated energy release process, i.e., triggering of repetitive magnetic reconnection, while the multiple periods might be modulated by the sausage oscillation of hot plasma loops. For the multi-periodic pulsations, other generation mechanisms could not be completely ruled out.