We propose a methodology for the treatment of the systematic model error in variational data assimilation. The principle of the method is to add a systematic error correction term in the model equations and to include it in the variational assimilation control vector. This method is applied to a simplified ocean circulation model in an identical twin experiment framework. It shows a noticeable improvement compared to the result of a classical variational assimilation scheme in which the systematic error is not corrected. The estimated systematic error correction term is sufficiently consistent with that needed by the model that it allows improvements not just to the analysis, but also during the forecast phase.