In this paper, the thermoelectric (TE) properties of Janus MXY monolayers (M = Pd, Pt; X, Y = S, Se, Te) are systematically studied using first principles and the Boltzmann transport theory. The thermal conductivity (k), Seebeck coefficient (S), power factor (PF), and TE figure of merit (ZT) are calculated accurately for various carrier concentrations. The lattice thermal conductivities of these six materials sequentially decrease in the order PtSSe, PtSTe, PtSeTe, PdSSe, PdSTe, and PdSeTe. PdSeTe and PtSeTe monolayers have a high ZT close to one at 300 K. In addition, we predicted the TE properties at high temperatures and found that the maximum ZT (2.54) is achieved for a monolayer of PtSeTe at 900 K. The structural and electronic properties of these six Janus transition-metal dichalcogenide (TMD) monolayers were systematically studied from first principles. Our results show that all six materials are semiconductors with bandgaps between 0.77 eV and 2.26 eV at the Heyd-Scuseria-Ernzerhof (HSE06) level. The present work indicates that the Janus MXY TMD monolayers (M = Pd, Pt; X, Y = S, Se, Te) are potentially TE materials.