Motivated by the synthesis of a Janus monolayer, the new PtSSe transition-metal dichalcogenide (TMD) have attracted remarkable attention due to their characteristic properties. In this work, we calculated the electronic structure, optical properties, and the thermal conductivity of the PtSSe monolayers, and performed a detailed comparison with other TMDs (monolayer PtS2 and PtSe2) using first-principles calculations. The calculated band gaps of the PtS2, PtSSe, and PtSe2 monolayers were 1.76, 1.38, and 1.21 eV, respectively, which are in good agreement with experimental data. At the same time, we observed a larger spin-orbit splitting in the electronic structure of PtSSe monolayers. The optical properties were also calculated and a significant red shift was observed from the PtS2 to PtSSe to PtSe2 monolayers. The lattice thermal conductivity of the PtSSe monolayer at room temperature (36.19 W/mK) is significantly lower than that of the PtS2 monolayer (54.25 W/mK) and higher than that of the PtSe2 monolayer (18.07 W/mK). Our results show that the PtSSe monolayer breaks structural symmetry and has the same ability to reduce the thermal conductivity as MoSSe and ZrSSe monolayers due to the shorter group velocity and the lower converged phonon scattering rate. These results may stimulate further studies on the electronic structure, optical properties, and thermal conductivity of the PtSSe monolayer in both experimental synthesis and theoretical efforts.