We propose a neural network (NN) predictor and an adaptive mode selection scheme for the purpose of both improving secondary user's (SU's) throughput and reducing collision probability to the primary user (PU) in full-duplex (FD) cognitive networks. SUs can adaptively switch between FD transmission-and-reception (TR) and transmission-and-sensing (TS) modes based on the NN prediction results for each transmission duration. The prediction performance is then analysed in terms of prediction error probability. We also compare the performance of our proposed scheme with conventional TR and TS modes in terms of SUs average throughput and collision probability, respectively. Simulation results show that our proposed scheme achieves even better SUs average throughput compared with TR mode. Meanwhile, the collision probability can be reduced close to the level of TS mode.