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In this paper, we investigate a large intelligent surface-enhanced (LIS-enhanced) system, where a LIS is deployed to assist secure transmission. Our design aims to maximize the achievable secrecy rates in different channel models, i.e., Rician fading and (or) independent and identically distributed Gaussian fading for the legitimate and eavesdropper channels. In addition, we take into consideration an artificial noise-aided transmission structure for further improving system performance. The difficulties of tackling the aforementioned problems are the structure of the expected secrecy rate expressions and the non-convex phase shift constraint. To facilitate the design, we propose two frameworks, namely the sample average approximation based (SAA-based) algorithm and the hybrid stochastic projected gradient-convergent policy (hybrid SPG-CP) algorithm, to calculate the expectation terms in the secrecy rate expressions. Meanwhile, majorization minimization (MM) is adopted to address the non-convexity of the phase shift constraint. In addition, we give some analyses on two special scenarios by making full use of the expectation terms. Simulation results show that the proposed algorithms effectively optimize the secrecy communication rate for the considered setup, and the LIS-enhanced system greatly improves secrecy performance compared to conventional architectures without LIS.