The increasing utilization of wind energy necessitates dedicated attentions to identify vulnerabilities, raise awareness, and formulate strategies for cybersecurity defense, response, and future protection. As a potential cyber attack, denial-of-service (DoS) attacks that block the communication between the rotor speed sensor and the controller of the wind turbine may overload the drive-train and reduce the power generation efficiency. This paper attempts to propose a dual-triggered resilient torque control strategy for the variable-speed wind turbine (VSWT) against DoS attacks. Therein, the mathematical models including the dynamics of the WT and the DoS attack are established, and a neural network observer is designed for the WT system to compensate for the signal losses caused by DoS attack. To guarantee the optimal rotor speed tracking of the WT, an adaptive torque control method based on dual-triggered mechanism is developed, and the attack tolerance capability of the WT system is evaluated. The proposed control strategy can largely enhance the attack resilience capability of the WT, while saving the resources of computation and communication. Extensive studies on a 1.5 MW WT illustrate that the proposed adaptive resilient control scheme can effectively mitigate the impact of the DoS attacks and guarantee the optimal rotor speed tracking performance for the WT system.