Broadband frequency-tripling pulses with high energy are attractive for scientific research, such as inertial confinement fusion, but are difficult to scale up. Third-harmonic generation via nonlinear frequency conversion, however, remains a trade-off between bandwidth and conversion efficiency. Based on gradient deuterium deuterated potassium dihydrogen phosphate (KDxH2-xPO4, DKDP) crystal, here we report the generation of frequency-tripling pulses by rapid adiabatic passage with a low-coherence laser driver facility. The efficiency dependence on the phase-matching angle in a Type-II configuration is studied. We attained an output at 352 nm with a bandwidth of 4.4 THz and an efficiency of 36%. These results, to the best of our knowledge, represent the first experimental demonstration of gradient deuterium DKDP crystal in obtaining frequency-tripling pulses. Our research paves a new way for developing high-efficiency, large-bandwidth frequency-tripling technology.