Maintaining system frequency at a rated value is a fundamental requirement to ensure the stability and security of power grids. However, the advanced frequency regulation process is more cyber-dependent, and raises a cyber-security issue for the power system. Traditional methods cannot avoid the adverse impacts of cyber attacks, which may lead to frequency deviations and, in severe cases, even blackouts. To address this issue, we propose an attack-resilient control algorithm for the smart grid's frequency regulation to defend the system frequency against cyber attacks. The stability of the system with the proposed controller can be guaranteed, which is strictly proved by Lyapunov theorem. Furthermore, the effectiveness of the proposed resilient controller is validated by case studies. The results show that in comparison with the existing methods, the proposed controller can make the system frequency achieve faster recovery with a minor frequency deviation. Specifically, using the proposed method, the maximum frequency deviation can be reduced from 0.17 Hz to approximately 0 Hz even under a cyber attack, which means that the adverse effects of a cyber attack can be almost eliminated. Therefore, the proposed controller can well counter potential cyber attacks, which helps improve the stability of the system frequency.