We predict that broadband efficient third-harmonic generation (THG) can be achieved with a frequency-doubling crystal and a novel composite KD*P triplet. The composite KD*P triplet is made of two partially deuterated KDP crystals with different deuteration levels by using the thermal bonding technique. The deuteration level of a partially deuterated KDP crystal is used as a degree of freedom to alter the phase-matching (PM) wavelength.Simulations show that the composite KD*P tripler can improve third-harmonic conversion efficiencies over a very wide band of input fundamental frequencies. In terms of robustness, alignment and stability, this THG scheme should be more promising than other broadband THG approaches because the composite KD*P tripler is a monolithic device.