In this paper, the downlink bit error rate (BER) performance of distributed antenna systems (DAS) with antenna selection over a composite fading channel is presented, where path loss, Rayleigh fading and lognormal shadowing are all considered for practicability. According to the performance analysis, and using the gamma distribution to approach log-normal distribution, an approximate closed-form expression of average BER is derived. This expression has a simple form and the value close to the actual simulation. To improve the accuracy of the BER further, we also derive a tightly approximate expression of cumulative distribution function (CDF) of the effective signal to noise ratio (SNR) by employing the numerical integrals. Based on this CDF, a tightly-approximate BER expression is achieved. All these theoretical expressions will provide good performance evaluation for DAS downlink. Simulation results show that the derived BER expressions are effective, and can match the corresponding simulations well, especially the second BER expression.