Novel Janus materials have attracted broad interest due to the outstanding properties created by their out-of-plane asymmetry, with increasing theoretical exploration and more reports of successful fabrication in recent years. Here, we construct and explore the crystal structures, stabilities, electronic band structures, and transport properties - including carrier mobilities - of two-dimensional Janus MGeSiP4 (M = Ti, Zr, or Hf) monolayers based on density functional theory calculations. From the cohesive energies, elastic constants, and phonon dispersion calculations, the monolayers are confirmed to exhibit structural stability with high feasibility for experimental synthesis. All the structures are indirect band-gap semiconductors with calculated band-gap energies in the range of 0.77 eV to 1.01 eV at the HSE06 (Heyd-Scuseria-Ernzerhof) level. Interestingly, by applying external biaxial strain, a semiconductor to metal phase transition is observed for the three Janus structures. This suggests potential for promising applications in optoelectronic and electromechanical devices. Notably, the MGeSiP4 monolayers show directionally anisotropic carrier mobility with a high electron mobility of up to 2.72 × 103 cm2 V-1 s-1 for the ZrGeSiP4 monolayer, indicating advantages for applications in electronic devices. Hence, the presented results reveal the novel properties of the 2D Janus MGeSiP4 monolayers and demonstrate their great potential applications in nanoelectronic and/or optoelectronic devices. This investigation could stimulate further theoretical and experimental studies on these excellent materials and motivate further explorations of new members of this 2D Janus family.