The electronic structure and magnetism of 4d TM-atom-doped h-GaTe monolayers were investigated through first-principles calculations. The results show that doped systems with Zr, Nb, Mo, Tc, Ru, Rh, and Pd atoms exhibit magnetism. Asymmetric orbital splitting caused by hybridization between the TM-4d and Te-5p orbitals is the main cause of magnetic generation. Under the influence of spin-orbit coupling (SOC), the Rh-doped system showed largest perpendicular magnetic anisotropy (PMA) of 3.56 meV/f.u. Most of the doped magnetic systems exhibit ferromagnetic coupling, with the exception of the Tc-doped system. The high Curie temperature of 327 K for Rh-doped system was calculated by Monte Carlo (MC) simulation, showing potential for achieving roomtemperature ferromagnetism. Under the combined influence of doping and biaxial strain, the magnetic semiconductor characteristics of Nb-doped system were maintained, with the magnetic moment remaining unchanged, whereas the properties of the other magnetic systems varied with strain, demonstrating the tuning effect of strain on the magnetic moment. This work provides important prospects for the application of h-GaTe in room-temperature spintronics.