At present, the research on two-dimensional (2D) ferromagnets is mainly concentrated on van der Waals materials, while the successful preparation of strain-free freestanding 2D perovskite films provides a great opportunity for designing 2D ferromagnets beyond van der Waals materials. Perovskite oxide SrRuO
3, a typical perovskite itinerant ferromagnet, has broad application prospects in many fields. In this work, 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 presents the structural phase (space group
P4/
mbm) generated by octahedral rotation distortion. Similar to the SrRuO
3bulk, Sr
2RuO
4has a monolayer ground-state phase that exhibits ferromagnetism, which is independent of the
Uvalue and thus robust. Density functional theory calculation using Hubbard parameter
Upredicts the ground-state phase of the monolayer to be a ferromagnetic half metal with an out-of-plane easy-magnetization axis, while excluding that 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 nor ferromagnetism of the Sr
2RuO
4monolayer, but can significantly modulate its electronic property and magnetic property. 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 developing perovskite-based 2D ferromagnets and realizing the control of 2D magnetism by electric field.