Two types of optimization methods were applied to a parameter optimization problem in a coupled ocean–sea ice model, and applicability and efficiency of the respective methods were examined. One is a finite difference method based on a traditional gradient descent approach, while the other adopts genetic algorithms as an example of stochastic approaches. Several series of parameter optimization experiments were performed by minimizing a cost function composed of model–data misfit of ice concentration, ice drift velocity and ice thickness. The finite difference method fails to estimate optimal parameters due to an ill-shaped nature of the cost function, whereas the genetic algorithms can effectively estimate near optimal parameters with a practical number of iterations. The results of the study indicate that a sophisticated stochastic approach is of practical use to a parameter optimization of a coupled ocean–sea ice model.