We report new limits on a spin-independent weakly interacting massive particle (WIMP)-nucleon interaction cross section using 39.5 kg days of data taken with a p-type point-contact germanium detector of 840 g fiducial mass at the Kuo-Sheng Reactor Neutrino Laboratory. Crucial to this study is the understanding of the selection procedures and, in particular, the bulk-surface events differentiation at the sub-keV range. The signal-retaining and background-rejecting efficiencies were measured with calibration gamma sources and a novel n-type point-contact germanium detector. Part of the parameter space in the cross section versus WIMP-mass implied by various experiments is probed and excluded.