A 994 g mass p-type PCGe detector has been deployed during the first phase of the China Dark matter EXperiment, aiming at direct searches for light weakly interacting massive particles. Measuring the thickness of the dead layer of a p-type germanium detector is an issue of major importance since it determines the fiducial mass of the detector. This work reports a method using an uncollimated ~(133)Ba source to determine the dead layer thickness. The experimental design, data analysis and Monte Carlo simulation processes, as well as the statistical and systematic uncertainties are described. A dead layer thickness of 1.02 mm was obtained based on a comparison between the experimental data and the simulated results.