The vessel arrival pattern is the basis of research on the port management including berth assignment, quay crane assignment and yard operations. The hypothesis that vessel arrival pattern follows the Poisson distribution (or the inter-arrival time of two consecutive vessel arrivals follows the exponential distribution) is regularly adopted by many researchers. This paper focuses on the vessel arrival pattern at the Hong Kong Port and examines the hypothesis mentioned above based on the real data. The chi-square test method is employed to check the hypothesis under the parameter the result shows the vessel arrival pattern does not follow the Poisson distribution. Researching into the arrival data, we find that there is peak time from 8 to 9 o’clock. Considering the peak time and normal time, respectively, we find that the vessel arrival pattern at both times follows the Poisson distribution. The conclusion is tested in different data set using the chi-square test.