Reconfigurable Intelligent Surface (RIS) draws great attentions in academic and industry due to its passive and low power consumption nature, and has currently been used in physical layer security to enhance the secure transmission. However, due to the existence of "double fading" effect on the reflecting channel link between transmitter and user, RIS helps achieve limited secrecy performance gain compared with the case without RIS. In this correspondence, we propose a novel active RIS design to enhance the secure wireless transmission, where the reflecting elements in RIS not only adjust the phase shift but also amplify the amplitude of signals. To solve the non-convex secrecy rate optimization based on this design, an efficient alternating optimization algorithm is proposed to jointly optimize the beamformer at transmitter and reflecting coefficient matrix at RIS. Simulation results show that with the aid of active RIS design, the impact of "double fading" effect can be effectively relieved, resulting in a significantly higher secrecy performance gain compared with existing solutions with passive RIS and without RIS design.