The Compact Pulsed Hadron Source (CPHS) has launched at Tsinghua University to develop a neutron source based on a 13-MeV, 50-mA proton linac, consisting of an ECR ion source, LEBT, RFQ, and DTL. The primary design of the DTL for the CPHS is presented in this paper, which includes the dynamics calculation, RF field optimization, and error analysis. This DTL accelerates a 50-mA proton beam from 3 MeV to 13 MeV with 1.2 MW of RF power. The DTL directly follows the RFQ with no Medium-Energy Beam-Transport line (MEBT). Transverse focusing is provided by PMQs housed in the drift tubes. The focusing lattice is designed to continue the transverse phase advance of the RFQ to preserve current independence while avoiding mismatches and parametric resonance