The China Dark matter Experiment collaboration reports the first experimental limit on WIMP dark matter from 14.6 kg-day of data taken with a 994 g p-type point-contact germanium detector at the China Jinping underground Laboratory where the rock overburden is more than 2400 m. The energy threshold achieved was 400 eVee. According to the 14.6 kg-day live data, we placed the limit of N= 1.75 * 10^{-40} cm^{2} at 90% confidence level on the spin-independent cross-section at WIMP mass of 7 GeV before differentiating bulk signals from the surface backgrounds.