A study for the weakly nonlinear wave height distribution for narrow banded random wave train show that the occurrence of probability of larger wave heights with the increasing of the value of kurtosis. The experimental data indicate good agreement with the Edgeworth-Rayleigh distribution with μ 3 ≪ 1 and μ 4 ≤ 4. However, the wave height distributions of the field data show discrepancies with the Edgeworth-Rayleigh distribution rather than the Rayleigh distribution, although the crest distribution show favorable agreement with the Edgeworth-Rayleigh distribution.