By performing first-principles calculations combined with the Boltzmann transport equation, we report a comprehensive study of the thermal and thermoelectric properties of monolayer triphosphides InP3, GaP3, SbP3 and SnP3. Firstly, we studied the structure and phonon dispersion, and discussed the long-range atomic interactions by analyzing the second-order interatomic force constants (IFCs). Next, we predicted the corresponding thermal conductivities of monolayer InP3, GaP3, SbP3 and SnP3 at 300 K to be 0.64 W m-1 K-1, 3.02 W m-1 K-1, 1.04 W m-1 K-1 and 0.48 W m-1 K-1, respectively. To study the thermoelectric properties, the carrier mobility and electron relaxation time of the four materials were predicted by the deformation potential theory method and explained by analyzing their energy band structures. Then, the Seebeck coefficient, electrical conductivity and thermoelectric figure of merit (ZT) at different temperatures were calculated by using the Boltzmann transport equation with relaxation time approximation. Finally, we predicted the maximum ZT values of InP3, GaP3, SbP3 and SnP3 to be up to 2.6, 0.9, 1.9 and 3.7 at 300 K and up to 4.6, 1.6, 3.5 and 6.1 at 500 K, respectively. With ultra-low thermal conductivity and high thermoelectric performance, monolayer triphosphides are considered as potential candidates for thermoelectric materials.