The traditional Markov prediction methods of the taxi destination rely only on the previous 2 to 3 GPS points. They negelect long-term dependencies within a taxi trajectory. We adopt a Recurrent Neural Network (RNN) to explore the long-term dependencies to predict the taxi destination as the multiple hidden layers of RNN can store these dependencies. However, the hidden layers of RNN are very sensitive to small perturbations to reduce the prediction accuracy when the amount of taxi trajectories is increasing. In order to improve the prediction accuracy of taxi destination and reduce the training time, we embed suprisal-driven zoneout (SDZ) to RNN, hence a taxi destination prediction method by regularized RNN with SDZ (TDPRS). SDZ can not only improve the robustness of TDPRS, but also reduce the training time by adopting partial update of parameters instead of a full update. Experiments with a Porto taxi trajectory data show that TDPRS improves the prediction accuracy by 12% compared to RNN prediction method in literature[4]. At the same time, the prediction time is reduced by 7%.