Benefiting from the joint learning of the multiple tasks in the deep multi-task networks, many applications have shown the promising performance comparing to single-task learning. However, the performance of multi-task learning framework is highly dependant on the relative weights of the tasks. How to assign the weight of each task is a critical issue in the multi-task learning. Instead of tuning the weights manually which is exhausted and time-consuming, in this paper we propose an approach which can dynamically adapt the weights of the tasks according to the difficulty for training the task. Specifically, the proposed method does not introduce the hyperparameters and the simple structure allows the other multi-task deep learning networks can easily realize or reproduce this method. We demonstrate our approach for face recognition with facial expression and facial expression recognition from a single input image based on a deep multi-task learning Conventional Neural Networks (CNNs). Both the theoretical analysis and the experimental results demonstrate the effectiveness of the proposed dynamic multi-task learning method. This multi-task learning with dynamic weights also boosts of the performance on the different tasks comparing to the state-of-art methods with single-task learning.