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A macro-spin simulation has been carried out to study the thermal stability of a spin-torque oscillator (STO) connected in parallel with a capacitance. To study the impact of realistic thermal fluctuation on an STO, a stochastic magnetic field vector is added into the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. From the numerical solution, it is found that the addition of capacitance positively influences the thermal stability of the system, and can improve the quality factor of the microwave power spectrum even in the presence of thermal fluctuation. The results of I-V phase shift under different conditions suggest that there may exist an optimum capacitance for which the thermal stability of the system can be most enhanced.