Compared to the pencil-beam algorithm, the Monte-Carlo (MC) algorithm is more accurate for dose calculation but time-consuming in proton therapy. To solve this problem, this study uses deep learning to provide fast 3D dose prediction for prostate cancer patients treated with intensity-modulated proton therapy (IMPT). A novel recurrent U-net (RU-net) architecture was trained to predict the 3D dose distribution. Doses, CT images, and beam spot information from IMPT plans were used to train the RU-net with a five-fold cross-validation. However, predicting the complicated dose properties of the IMPT plan is difficult for neural networks. Instead of the peak-monitor unit (MU) model, this work develops the multi-MU model that adopted more comprehensive inputs and was trained with a combinational loss function. The dose difference between the prediction dose and Monte Carlo (MC) dose was evaluated with gamma analysis, dice similarity coefficient (DSC), and dose-volume histogram (DVH) metrics. The MC dropout was also added to the network to quantify the uncertainty of the model. Compared to the peak-MU model, the multi-MU model led to smaller mean absolute errors (3.03% vs. 2.05%, p = 0.005), higher gamma-passing rate (2 mm, 3%: 97.42% vs. 93.69%, p = 0.005), higher dice similarity coefficient, and smaller relative DVH metrics error (clinical target volume (CTV) D98% : 3.03% vs. 6.08%, p = 0.017; in Bladder V30: 3.08% vs. 5.28%, p = 0.028; and in Bladder V20: 3.02% vs. 4.42%, p = 0.017). Considering more prior knowledge, the multi-MU model had better-predicted accuracy with a prediction time of less than half a second for each fold. The mean uncertainty value of the multi-MU model is 0.46%, with a dropout rate of 10%. This method was a nearly real-time IMPT dose prediction algorithm with accuracy comparable to the pencil beam (PB)analytical algorithms used in prostate cancer. This RU-net might be used in plan robustness optimization and robustness evaluation in the future.