In this paper, we analyze the secrecy performance of the decode-and-forward (DF) relay system in generalized-K fading channels. In a typical four-node communications model, a source (S) sends confidential information to a destination (D) via a relay (R) using DF strategy in two time slots, while an eavesdropper (E) wants to overhear the information from S to D over generalized-K fading channels. To be more realistic, we assume that E can receive the signals of two time slots, and there is no direct link between S and D because of heavy fading. Based on those assumptions, we derive closed-form expressions for the secrecy outage probability (SOP) and ergodic secrecy capacity (ESC) by using a tight approximate probability density function of the generalized-K model. Then, asymptotic expressions for the SOP and ESC are also derived in the high signal-to-noise ratio region, not only because we can get some insights about SOP and ESC, but also because expressions for SOP and ESC can be simplified significantly. The single relay system is subsequently extended into a multi-relay system, where the asymptotic SOP analysis of three proposed relay selection strategies is investigated. Further, the security-reliability tradeoff analysis in the multi-relay system is also presented given that S adopts a constant code rate. Finally, the Monte-Carlo simulation is used to demonstrate the accuracy of the derived closed-form expressions.