A kind of multi-input and multi-output network control system with multiple independent control loops is examined in this paper. The controller of each control loop is connected with the sensor and actuator by a network and each control loop has a different sampling period. The whole mathematical model of this kind of networked control system is set up when the maximum network-induced delay is smaller than one sampling period. And the sufficient condition subject to the asymptotic stability of this kind of networked control system is derived based on the theorem for estimation of feature value deduced from perturbation theory. The research results of this paper have significance in the analysis and design of this kind of networked control system or a similar networked control system.