We carried out deep mapping observations of the atomic hydrogen (H I) 21 cm line emission in a field centered on the famous galaxy group Stephan's Quintet (SQ), using the Five-hundred-meter Aperture Spherical Telescope (FAST) equipped with a 19-beam receiver. The final data cube reaches an H I column density sensitivity of 5 sigma = 2.1 x 10(17) cm(-2) per 20 km s(-1) channel with an angular resolution of 4 ' 0. The discovery of a large diffuse feature of the H I emission in the outskirts of the intragroup medium of SQ was reported in a previous paper (Xu et al.). Here we present a new study of the total H I emission of SQ and the detection of several neighboring galaxies, exploiting the high sensitivity and the large sky coverage of the FAST observations. A total H I mass of M-H I = 3.48 +/- 0.35 x 10(10) M-circle dot is found for SQ, which is significantly higher than previous measurements in the literature. This indicates that, contrary to earlier claims, SQ is not H I deficient. The excessive H I gas is mainly found in the velocity ranges of 6200-6400 km s(-1) and 6800-7000 km s(-1), which were undetected in previous observations that are less sensitive than ours. Our results suggest that the missing H I in compact groups may be hidden in the low-density diffuse neutral gas instead of in the ionized gas.