Abstract: As a result of an increased share of renewable energy and the retirement of gas turbine generators, the challenge of maintaining frequency stability in offshore oilfield power systems (OOPSs) has become increasingly notable. To mitigate these challenges, grid-forming (GFM) energy storage offers a promising solution. To study the frequency stability of OOPSs with GFM energy storage, this paper first clarifies its control strategy, considering both converter control parameters and the response speed of gas turbine governors. Then, based on the power-frequency-rotor angle relationship of the GFM energy storage and OOPSs, an equivalent frequency response model is constructed. This equivalent model is subsequently simplified, and its closed form solution is determined. The frequency stability is then examined in terms of rate of change of frequency, frequency nadir, system inertia, and frequency fluctuation. The effects of the inertia parameter, frequency modulation coefficient and virtual impedance are determined. Finally, using an actual OOPS as the example, the effectiveness of the proposed method is validated through simulation. The study further analyzes the distinctions in frequency support capabilities between grid-following (GFL) and GFM energy storage, which aims to provide a reference for the renewable-dominant OOPSs.