In this paper, we perform transmit antenna selection to improve the energy efficiency of large scale multiple antenna systems. We derive a good approximation of the distribution of the mutual information in this antenna selection system. It shows that channel hardening phenomenon is still retained as full complexity with antenna selection. Then, we use this closed-form expression to assess the energy efficiency performance. Specifically, we evaluate the performance of the energy efficiency in two different cases: 1) the circuit power consumption is comparable to or even dominates the transmit power, and 2) the circuit power can be ignored due to relatively much higher transmit power. The theoretical analysis indicates that there exists an optimal number of selected antennas to maximize the energy efficiency in the first case, whereas in the second case, the energy efficiency is maximized when all the available antennas are used. Based on these conclusions, two simple but efficient antenna selection algorithms are proposed to obtain the maximum energy efficiency. All the analytical results are verified through computer simulations.