In studies of potential wind energy, knowing statistical distribution of wind direction provides useful information in making predictions and gives a better understanding of the behavior of the wind direction. Malaysia experiences two monsoon seasons per year, namely Southwest Monsoon and Northeast Monsoon and in this paper, our interest is to investigate whether the direction of wind data in monsoon seasons can be modelled using replicated LFRM with von Mises distribution. The beauty of this model is that it considers the error terms in both x and y variables. This study considers the bivariate relationship of directional wind data where errors are present in both. Here, we propose a replicated functional relationship model, with the von Mises distribution to describe the relationship of the wind direction data. In the parameter estimation, maximum likelihood method is considered with pseudo-replicated group of the replicated form of the functional relationship. The novelty of this approach is that assumption on the ratio of concentration parameters is no longer deemed necessary. Also, we derive the covariance matrix of the parameters based on Fisher Information. From the Monte Carlo simulation study, small bias measures were obtained, suggesting the viability of the model. Based on the simulation study, it can be concluded that the wind direction of the two monsoons in Malaysia can be modelled using replicated linear functional relationship model.