In order to continue to provide high quality communication services, mobile network operators want to detect the degradation of the communication quality when it occurs. Since actively evaluating LTE network performance is costly and time consuming, mobile network operators passively monitor the network. A finite state machine is a powerful approach for monitoring the network condition. However, in actual LTE network, it is not sufficient to validate the conformance between the specification machine and the implementation machine. Therefore, this paper proposes a LTE network monitoring method using statistics of state transition. In the proposed method, we first define the states according to 3GPP standards, then, we measure the state transition by referring to LTE C-Plane messages. Also, we measure the state transition probability and time interval for the transition. Finally we check the statistics of the state transition to detect the degradation of the communication quality. In order to evaluate the proposed method, we introduce an example of detecting ping-pong handovers using actual traffic data. We show the potential usefulness of the proposed method for practical use.