Flight Trajectory Prediction (TP) is an essential task in Air Traffic Control (ATC). Currently, the TP task is usually achieved by regression approaches, which concatenates several scalar attributes of the observation into a low-dimensional vector as the inputs. However, it is difficult to accurately model aircraft motion patterns using low-dimensional features in complex and time-varying ATC environments. To improve the performance of the TP task, in this paper, a novel framework, called FlightBERT, is proposed based on Binary Encoding (BE) representation, which enables us to tackle the TP task as a multi binary classification problem. Specifically, the scalar attributes of the flight trajectory are encoded into binary codes and transformed into a high-dimensional representation by the attribute embedding module. Considering the prior knowledge among flight attributes, an Attribute Correlation Attention (ACoAtt) block is designed to explicitly capture the correlations among the specific attributes. A stacked Transformer block is applied to serve as the backbone network, which is followed by the predictor to generate the outputs. Considering the nature of flight trajectory, a hybrid constrained loss, i.e., combining the mean square error loss with the binary cross-entropy loss, is innovatively designed to optimize the proposed framework. The proposed method is validated on a large-scale dataset, which is collected from the real-world ATC environment. The experimental results demonstrate that the proposed method outperforms other baselines by quantitative and qualitative evaluations.