It is a significant task to predict the solar activity for space weather and solar physics. All kinds of approaches have been used to forecast solar activities, and they have been applied to many areas such as the solar dynamo of simulation and space mission planning. In this paper, we employ the long-short-term memory (LSTM) and neural network autoregression (NNAR) deep learning methods to predict the upcoming 25th solar cycle using the sunspot area (SSA) data during the period of May 1874 to December 2020. Our results show that the 25th solar cycle will be 55% stronger than Solar Cycle 24 with a maximum sunspot area of 3115 +/- 401 and the cycle reaching its peak in October 2022 by using the LSTM method. It also shows that deep learning algorithms perform better than the other commonly used methods and have high application value.