A multivariate Markov chain model is presented for generating sea state time series based on observed time series. The sea state is represented by the wave height, wind speed, wave period, wind direction and wave direction. Two ways of capturing the seasonal variation in the sea state parameters resulted in two distinct models. Their quality was assessed by comparing their statistical properties to what was obtained from observed time series. In one of the models (Model 1) transition probabilities were estimated separately for each month, while in the other (Model 2) a monthly transformation of the data were performed. Two different sea state data sets were considered in the validation, and it was found that both models compared favorably to the empirical data. It was concluded that Model~1 worked best for the longest data set considered, but was challenged by the shorter time series, where Model~2 worked best. Model 2 uses the observed data more efficiently, but relies on stationarity after removing the monthly variability, which seems to be a reasonable approximation for the data considered. The effect of changing the wave height resolution in the modeled time series was also investigated.