In this paper a novel method is proposed to estimate the rotor speed of synchronous generators in steady state and dynamic conditions using phasor measurement unit's data. This method uses the synchronous generator model to find the relationship between generator rotor speed and frequencies at different buses of the power system. The principles of the proposed method are first presented through a simple network consisting a generator connected to a transmission line. Afterward the general formulation is developed. To demonstrate the effectiveness of our method, IEEE 9-bus and IEEE 39-bus power systems are used as the benchmark systems. Different tests are carried out under three conditions including, normal condition, presence of measurement errors and uncertainty of the power system parameters. As well, the estimation results are compared with the results of other estimation methods. The results show the high accuracy of the proposed method in different conditions.