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Neutral hydrogen (HI) is the fundamental component of the interstellar medium. The Galactic Plane Pulsar Snapshot (GPPS) survey is designed for hunting pulsars by using the Five-hundred-meter Aperture Spherical radio Telescope (FAST) from the visible Galactic plane within $|b| \leq 10^{\circ}$. The survey observations are conducted with the L-band 19-beam receiver in the frequency range of 1.0 $-$ 1.5 GHz, and each pointing has an integration time of 5 minutes. The piggyback spectral data simultaneously recorded during the FAST GPPS survey are great resources for studies on the Galactic HI distribution and ionized gas. We process the piggyback HI data of the FAST GPPS survey in the region of $33^{\circ} \leq l \leq 55^{\circ}$ and $|b| \leq 2^{\circ}$. The rms of the data cube is found to be approximately 40 mK at a velocity resolution of $0.1$ km s$^{-1}$, placing it the most sensitive observations of the Galactic HI by far. The high velocity resolution and high sensitivity of the FAST GPPS HI data enable us to detect weak exquisite HI structures in the interstellar medium. HI absorption line with great details can be obtained against bright continuum sources. The FAST GPPS survey piggyback HI data cube will be released and updated on the web: http://zmtt.bao.ac.cn/MilkyWayFAST/.