Rate of penetration has been considered as an important factor in the entire drilling industry, which can largely determine the overall costs of drilling a well. This paper proposed a novel real-time prediction of rate of penetration by combining the Attention-based Bidirectional-Long Short-Term Memory and Long Short-Term Memory (Att-Bi-LSTM-LSTM). Eight parameters, which are total vertical depth, weight on bit, revolutions per minute, mud flow rate, density, viscosity, drill-bit outer-diameter, lithology, and rate of penetration, are adopted as datasets. The drilling speed of the well is trained and validated through the drilling data while a sliding window is introduced for the real-time update. In addition, the presented prediction model is compared with other traditional prediction methods. Finally, the prospect of field application and further study is discussed and suggested. The results indicate that the proposed model shows good accuracy and robustness. Moreover, compared with the traditional methods, the model exhibits good superiority with smaller absolute and relative errors. For field applications, the model proposed in this paper attempts to provide a solution to the prediction of real-time rate of penetration. The results are expected to provide guidance for the further study on the increase of drilling speed and reduction of well costs.