Variations of solar activity are a result of a complicate dynamo process in the convection zone. We consider this phenomenon in the context of sunspot number variations, which have detailed observational data during the past 23 solar cycles. However, despite the known general properties of the solar cycles a reliable forecast of the 11-year sunspot number is still a problem. The main reasons are imperfect dynamo models and deficiency of the necessary observational data. To solve this problem we propose to use data assimilation methods. These methods combine observational data and models for best possible, efficient and accurate estimates of physical properties that cannot be observed directly. The methods are capable of providing a forecast of the system future state. It is demonstrated that the Ensemble Kalman Filter (EnKF) method can be used to assimilate the sunspot number data into a non-linear α-Ω mean-field dynamo model, which takes into account dynamics of turbulent magnetic helicity. We apply this method for characterization of the solar dynamo properties and for prediction of the sunspot number.