Multi-modal semantic trajectory prediction has become a new challenge due to the rapid growth of multi-modal semantic trajectories with text message. Traditional RNN trajectory prediction methods have the following problems to process multi-modal semantic trajectory. The distribution of multi-modal trajectory samples shifts gradually with training. It leads to difficult convergency and long training time. Moreover, each modal feature shifts in different directions, which produces multiple distributions of dataset. To solve the above problems, MNERM (Mode Normalization Enhanced Recurrent Model) for multi-modal semantic trajectory is proposed. MNERM embeds multiple modal features together and combines the LSTM network to capture long-term dependency of trajectory. In addition, it designs Mode Normalization mechanism to normalize samples with multiple means and variances, and each distribution normalized falls into the action area of the activation function, so as to improve the prediction efficiency while improving greatly the training speed. Experiments on real dataset show that, compared with SERM, MNERM reduces the sensitivity of learning rate, improves the training speed by 9.120 times, increases HR@1 by 0.03, and reduces the ADE by 120 meters.