Rotor imbalances of a wind turbine can cause severe damage of the turbine or its components and thus reduce the lifespan and security of the turbine significantly. At present, balancing of the rotor is a time consuming and expensive process due to the necessity of mounting test weights to measure a reference imbalance state. We describe a new method for the detection and reconstruction of imbalances in the rotor of a wind turbine avoiding test weight measurements. The method is based on a wind turbine model, which is derived by the finite element method. In some respect, the model information replaces the information of a reference imbalance state. A mathematical equation linking imbalances and the resulting vibrations is derived using the model. Thus the inverse problem of computing an imbalance from vibration measured at the nacelle is solvable with the usual techniques for ill-posed problems. We show that our model for a wind turbine can be used to predict the vibrations for a given imbalance distribution. In particular, it can be used to reconstruct the imbalance distribution of a wind turbine from noisy measurements in real time, which is verified both for artificial and real data. Also, an optimization strategy is presented in order to adapt the model to the wind turbine at hand. The new method requires a simple model of a wind turbine under consideration but reduces the measuring effort for the computation of balancing weights. It can be implemented into a condition monitoring system (CMS). For the first time, there can be not only an alarm generation but also the actual imbalance and balancing weights and positions can be computed directly from the observed CMS data.