The long-range correlation of nodes in a computer network model is studied with the mean square fluctuation function of cumulative variable of queue lengths. It is shown that the queue lengths of the data packets of nodes change their temporal independence on or short-range correlation in the free flow state to long-range correlation in the critical and congested state with increasing system loading. The range of correlation enlarges and the collective long-range correlation emerges. In a free flow, the nodes are independent of each other or short-range correlative, and there exists a typical characteristic power exponent of 0.5. At the critical state, the nodes are long-range correlative, and there exists a typical characteristic power exponent bigger than 0.5. Moreover, the collective interaction becomes obvious and the power exponent decreases with enlarging network scale.