Broadband frequency-tripling pulses with high energy are attractive for scientific research such as inertial confinement fusion (ICF), but are difficult to scale up. Third-harmonic generation (THG) 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 (RAP) with low-coherence laser driver facility. The efficiency dependence on phase matching (PM) angle in 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, represents 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.