The Maximum Entropy Principle (MEP) method is elaborated, and the corresponding probability density evaluation method for the random fluctuation system is introduced, the goal of the article is to find the best fitting method for the wave climate statistical distribution. For the first time, a kind of new maximum entropy probability distribution (MEP distribution) expression is deduced in accordance with the second order moment of a random process. Different from all the fitting methods in the past, the MEP distribution can describe the probability distribution of any random fluctuation system conveniently and reasonably. If the moments of the random signal is limited to the second order, that is, the ratio of the root-mean-square value to the mean value of the random variable is obtained from the random sample, the corresponding MEP distribution can be computed according to the deduced expression in this essay. The concept of the wave climate is introduced here, and the MEP distribution is applied to fit the probability density distributions of the significant wave height and spectral peak period. Take the Mexico Gulf as an example, three stations at different locations, depths and wind wave strengths are chosen in the half-closed gulf, the significant wave height and spectral peak period distributions at each station are fitted with the MEP distribution, the Weibull distribution and the Log-normal distribution respectively, the fitted results are compared with the field observations, the results show that the MEP distribution is the best fitting method, and the Weibull distribution is the worst one when applied to the significant wave height and spectral peak period distributions at different locations, water depths and wind wave strengths in the Gulf. The conclusion shows the feasibility and reasonability of fitting wave climate statistical distributions with the deduced MEP distributions in this essay, and furthermore proves the great potential of MEP method to the study of wave statistical properties.