Density functional theory calculations are performed in order to study the structural and electronic properties of monolayer Pt2HgSe3. Our results show that the dynamically stable monolayer Pt2HgSe3 is a topological insulator with a band gap of 160 meV. In addition, the effect of layer thickness, strain and electric field on the electronic properties are systematically investigated using fully relativistic calculations. We find that the electronic properties are sensitive to the applied electric field. With increasing electric field strength up to 0.5 V Å-1, the band gap decreases from 160 to 10 meV at 0.5 V Å-1. Interestingly, upon further increasing the electric field up to 1.0 V Å-1, the band gap opens again and reaches its bare value (160 meV) at 1.0 V Å-1, which indicates that the band gap is reversibly controllable via the applied external electric field. Moreover, the electronic properties are also examined under uniaxial and biaxial strain. Our results reveal that the band gap value can be tuned to 150 meV (at 1%) and to 92 meV (at 6%) under uniaxial strain, while under biaxial tensile strain, it increases to 170 meV at 5% and fluctuates between 150 and 100 meV in the range of 5-10%. In contrast, the biaxial-compressive strain is found to drive the semiconducting-to-metallic transition for sufficiently large compressions (over 8%). On the other hand, we find that increasing the thickness of Pt2HgSe3 modifies the band gap to 150 meV (for the bilayer) and 140 meV (for the trilayer). In the bilayer Pt2HgSe3 structure, we further investigated the effect of out-of-plane pressure, both compressive and tensile, and our results show that the electronic structure of bilayer Pt2HgSe3 is largely preserved. Our study provides new insight into the modification of the electronic structure of monolayer Pt2HgSe3 upon application of external fields and variation in the layer thickness.