  We investigate the 1/f noise of the Five-hundred-meter Aperture Spherical
Telescope (FAST) receiver system using drift-scan data from an intensity
mapping pilot survey. All the 19 beams have 1/f fluctuations with similar
structures. Both the temporal and the 2D power spectrum densities are
estimated. The correlations directly seen in the time series data at low
frequency $f$ are associated with the sky signal, perhaps due to a coupling
between the foreground and the system response. We use Singular Value
Decomposition (SVD) to subtract the foreground. By removing the strongest
components, the measured 1/f noise power can be reduced significantly. With 20
modes subtraction, the knee frequency of the 1/f noise in a 10 MHz band is
reduced to $1.8 \times 10^{-3}\Hz$, well below the thermal noise over
500-seconds time scale. The 2D power spectra show that the 1/f-type variations
are restricted to a small region in the time-frequency space and the
correlations in frequency can be suppressed with SVD modes subtraction. The
residual 1/f noise after the SVD mode subtraction is uncorrelated in frequency,
and a simple noise diode frequency-independent calibration of the receiver gain
at 8s interval does not affect the results. The 1/f noise can be important for
HI intensity mapping, we estimate that the 1/f noise has a knee frequency
$(f_{k}) \sim$ 6 $\times$ 10$^{-4}$Hz, and time and frequency correlation
spectral indices $(\alpha) \sim 0.65$, $(\beta) \sim 0.8$ after the SVD
subtraction of 30 modes. This can bias the HI power spectrum measurement by 10
percent.
