We present results on light weakly interacting massive particle (WIMP) searches with annual modulation (AM) analysis on data from a 1-kg mass p-type point-contact germanium detector of the CDEX-1B experiment at the China Jinping Underground Laboratory. Datasets with a total live time of 3.2 yr within a 4.2-yr span are analyzed with analysis threshold of 250 eVee. Limits on WIMP-nucleus (χ-N) spin-independent cross sections as function of WIMP mass (m_{χ}) at 90% confidence level (C.L.) are derived using the dark matter halo model. Within the context of the standard halo model, the 90% C.L. allowed regions implied by the DAMA/LIBRA and CoGeNT AM-based analysis are excluded at >99.99% and 98% C.L., respectively. These results correspond to the best sensitivity at m_{χ}<6 GeV/c^{2} among WIMP AM measurements to date.