Adding noise to the covert timing channel is an important method to decrease the covert channel's capacity. Most works are focus on the first in first out queuing for service mechanism, but the mechanism restricts the network packet transfer rate. This paper analyzes the network covert timing channel with artificial noise which is uniformly distributed. The mechanism of adding noise is not queuing, and it doesn't restrict the network packet transfer rate. Paper gets a series formulas to calculate the channel's capacity, and calculates the channel's capacity in some special situations. The analysis shows the relationship between the noise intensity and the channel's capacity. To verify the correctness of the theory analysis, paper constructs such a network covert timing channel, and the channel's communication performance is in accord with the theory analysis.