Observations have revealed the widespread distribution of internal waves in deep oceans, shallow seas, lakes and reservoirs. Much theoretical, numerical, laboratory and field work has studied their generation and propagation, and in particular significant progress has been made in internal solitary wave research. However, statistical properties of internal waves, especially in shallow water, are still little understood. This paper is to investigate the second-, third- and fourth-order moments of internal waves. Results of internal waves in a strong seasonal thermocline of the Yellow Sea are presented and analyzed. It is found that the skewness coefficients are nonzero and the kurtosis coefficients are greater than 3, indicating skewed waveshapes and non-Gaussian distributions of the internal wave elevations. Statistics have been widely used to describe nonbreaking shoaling sea surface waves. It is suggested that the present study on internal gravity waves could be extended to construct nonlinear models for shallow-water internal waves. [Work supported by NSFC.]