Recently, unmanned aerial vehicles (UAVs) have gained significant popularity and have been extensively utilized in wireless communications. Due to the susceptibility of wireless channels to eavesdropping, interference and other security attacks, UAV communication security faces serious challenges. Therefore, novel solutions need to be investigated for handling corresponding issues. Note that the UAV with full-duplex (FD) mode can actively improve spectral efficiency, and reconfigurable intelligent surface (RIS) can enable the intelligent control of signal reflection for improving transmission quality. Accordingly, the security of UAV communications may be considerably improved by combining the two techniques mentioned above. In this paper, we investigate the performance of secure communication in urban areas, assisted by a FD UAV and an RIS, where the UAV receives sensitive information from the ground users and sends jamming signals to the ground eavesdroppers. Particularly, we propose an approach to jointly optimize the user scheduling, user transmit power, UAV jamming power, RIS phase shift, and UAV trajectory for maximizing the worst-case secrecy rate. However, the non-convexity of the problem makes it difficult to solve. Combining alternating optimization (AO), slack variable techniques, successive convex approximation (SCA), and semi-definite relaxation (SDR), we propose an effective algorithm to obtain a suboptimal solution. According to the simulation results, in contrast to other benchmark schemes, we show that our proposed algorithm can significantly improve the overall secrecy rate.