Recently, inferring lane change intention has received considerable attention. Due to the high nonlinearity and complexity of traffic contexts, traditional methods cannot satisfy the requirements of long-term prediction tasks and lack the ability of capturing nonlinear temporal dependencies. This paper proposes an intention inference model based on Recurrent Neural Networks (RNN), to tackle time series prediction problems. Considering dynamic interaction among surrounding vehicles, our model takes the sequence motion information of surrounding vehicles as inputs and calculates the congestion of different lanes, integrated with vehicle states of the object vehicle. To illustrate the availability of the proposed RNN intention inference model, a motion planning controller considering intention was developed. A Nonlinear Model Predictive Control (NMPC) was established to planning a safe, sub-optimal path for autonomous driving vehicle under collision avoidance constraints. The experiments on the proposed model were conducted, based on two RNN structure Long-Short Term Memory (LSTM) and Generalized Recurrent Unit (GRU), by Tensorflow with NGSIM data. The motion planning controller is modeled and simulated by Carsim with Simulink for some typical scenarios. Subsequently, experimental results demonstrate that RNN achieves best performance, inferring intention with 96% accuracy, compared with other approaches.