Concerning the network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/G/1 queuing system model was proposed. Firstly, as the parameter n of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of total probability theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained. Simulation under Matlab 2010a showed that, the mean absolute error between average waiting time and theoretical formula results at all levels of queue, was just 0.951%. In the experiment, the average waiting time ratio with limited-priority was significantly smaller than the average waiting time ratio with full priority at all levels of queue. The experimental results show that the theoretical results, which use the nonpreemptive limited-priority M/G/1 queuing system model, are correct; besides, the model is more stable than the others.