Distributed antenna system (DAS) is one of the most promising candidates for future wireless communications. Despite an increasing amount of academic attention, the channel models of DAS in previous work lack generality. In this paper, we present a more generic channel model, which takes path loss, lognormal shadowing and Generalized-Gamma fast fading into consideration. This composite channel model includes many well-known composite channel models as special cases. Based on the channel model and the distribution of mobile station (MS) in the cell, an approximate theoretical expression of system outage probability is derived by using selective transmission (ST) scheme. Numerical results show that the approximate expression can provide sufficient precision for evaluating the outage performance of DAS.