At present, the research on two-dimensional (2D) ferromagnets is mainly concentrated in the field of van der Waals materials, while the successful preparation of strain-free freestanding 2D perovskite films provides a great opportunity for the design of 2D ferromagnets beyond van der Waals materials. Perovskite oxide SrRuO ₃, as a typical perovskite itinerant ferromagnet, has broad application prospects in many fields. In this paper, the lattice dynamics, ground-state structure, electronic and magnetic properties of its perovskite monolayer with formula Sr ₂RuO ₄, as well as the effect of external electric field, are studied by combining first-principles calculation, symmetry analysis and Monte Carlo simulation. The influence of the Hubbard parameter Uis also revealed. The results indicate that the ground-state structure under all Uvalues is the structural phase (space group $P4/mbm$) generated by octahedral rotation distortion. Similar to the SrRuO ₃bulk, the ground-state phase of the Sr ₂RuO ₄monolayer exhibits ferromagnetism, which is independent of the Uvalue and thus robust. Density functional theory calculation with Hubbard parameter Upredicts the ground-state phase of the monolayer to be a ferromagnetic half metal with out-of-plane easy-magnetization axis, while excluding the Uparameter predicts the ground-state phase to be a ferromagnetic metallic state. The ferromagnetism mainly originates from the strong ferromagnetic exchange interaction between the nearest neighbor spin pairs. The simulated Curie temperature of the Sr ₂RuO ₄monolayer is 177 K, which is close to the value (150 K) of its bulk phase. The out-of-plane electric field does not change the ground-state structure and ferromagnetism of the Sr ₂RuO ₄monolayer, but can significantly modulate its electronic and magnetic properties. When an external electric field exceeding 0.3 V/Å is applied, the system undergoes a transition from a ferromagnetic half-metal state to a ferromagnetic metallic state. This work indicates the potential application of Sr ₂RuO ₄monolayer in low-dimensional spintrnic devices, and provides a reference for the development of perovskite-based 2D ferromagnets and the realization of controlling 2D magnetism by electric field.