In this paper, we propose a hybrid precoding scheme for high altitude platform (HAP) massive multiple-input multiple-output (MIMO) systems with limited RF chains. In the proposed scheme, we formulate the RF precoder design problem as an average signal-to-leakage-and-noise ratio (SLNR) maximization problem, where the RF precoder is selected from a discrete codebook. First, we obtain the lower bound of the average SLNR and transform it into a trace problem. Then, for ease of handling, signal-to-leakage ratio (SLR) is adopted to achieve the initial RF precoder. Finally, a greedy algorithm for RF precoding is proposed to update the initial RF precoder for better performance.