This article considers the problem of periodic event-triggered control design for dual-rate networked control systems subject to nonvanishing disturbance. The plant considered in this article is a kind of dual-rate networked control system, where the sensor samples the measurement output at a slow rate and the actuator updates the control input at a fast rate. Despite the slow-rate sampling of the sensor, a new output predictor-based observer is proposed to accurately estimate system state and disturbance in the intersample time interval, and an active anti-disturbance controller that updates at a fast rate is accordingly proposed, such that the desirable control performance and disturbance rejection performance can be achieved. At each fast-rate updating time instant, we use the prediction technique to generate a data packet, including the computed current control input and the predicted values of the control inputs for the future finite steps, and design a new periodic event-triggered mechanism to determine whether to transmit the data packet via a communication network or not. The proposed control method is easily implemented in digital platform since it has a discrete-time form. To verify the effectiveness of the proposed control method, we finally present the simulation results of a practical speed control system.