With the development of the economy and technology, people’s requirement for communication is also increasing. Satellite networks have been paid more and more attention because of its broadband service capability and wide coverage. In this paper, we investigate the framework of a long-short term memory (LSTM) and transfer learning-based Combined Free/Demand Assignment Multiple Access (CFDAMA) scheme (CFDAMA-LSTMTL), which is a new multiple access scheme in the broadband satellite system. Generally, there is a delay time T between sending a request from the user to the satellite and receiving a reply from the satellite. So far, the traditional multiple access schemes has not processed the data traffic generated in this period of time. So, in order to transmit the data traffic in time, we propose a new prediction method, which combines LSTM with transfer learning. We introduce the prediction method into the CFDAMA scheme so that it can reduce data accumulation by the way of sending the sum slots requested by the user and the predicted request slots generated in the delay time T. A comparison with CFDAMA-PA and CFDAMA-PB is provided through simulation results, which gives the effect of the CFDAMA-LSTMTL in a broadband satellite systems.