A variational data assimilation method is applied to a simplified marine ecosystem model of NPZ (Nutrient Phytoplankton Zooplankton) type, which implies five parameters. The method allows us to optimise these parameters by an iterative process of minimisation of a cost function which quantifies the quadratic discrepancy between observations and simulation results. The first part of this note describes how to obtain the adjoint model of the NPZ model allowing us to compute the gradient of the cost function relative to the parameters. Two experiments of artificial data assimilation then show the efficiency of this method, but also its limitations because of non-linearities and sensitivity problems of the model relative to the parameters.