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Probabilistic wave model is not only more suitable to describe uncertainties affecting structural reliability than deterministic wave model but also used to calculate probabilistic motion and structural response, which are able to facilitate the evaluation of structural reliability. In this regards, efforts have been made in this research to estimate the probabilistic wave spectrum using onboard measurement data. Firstly, Markov chain Monte Carlo simulation, which archives sampling from arbitrary probability density function of wave parameter as a random variable, was adopted as a probabilistic optimization method. Prior distribution and constraints of wave parameter were defined according to design wave model and previous wave observations. Previous wave observations consist of full-scale measurements obtained from 14,000 TEU container ship and MetOcean data of actual sea. Secondly, Numerical case study was performed for checking the validity of the proposed method. Data based on numerical simulations were generated by combining assumed wave spectrum and response amplitude operator, with some noise added. Finally, the proposed method was applied to full-scale measurements gathered from 14,000 TEU container ship, then, the calculated wave spectrum, motion and structural response were compared with full-scale measurements.