We consider solar magnetic activity in the context of sunspot number variations, as a result of a non-linear oscillatory dynamo process. The chaotic behavior of the sunspot cycles and undefined errors of observations create uncertainties for predicting the strength of the cycles. Uncertainties in some dynamo model parameters create additional difficulties for the forecasting. The modern data assimilation methods allow us to assimilate the observational data into the models for possible efficient and accurate estimations of the physical properties, which cannot be observed directly. We apply the Ensemble Kalman Filter method to a low-order non-linear dynamo model, which takes into account variations of the turbulent magnetic helicity and reproduces the basic characteristics of the solar cycles. We investigate the predictive capabilities of this approach, and present test results for prediction of the previous cycles and a forecast of the next solar cycle 24.