Massive multiple-input multiple-output (MIMO) techniques have been recently advanced to tremendously improve the performance of wireless networks. However, the use of very large antenna arrays brings new issues, such as the significantly increased hardware cost and signal processing cost and complexity. In order to reap the enormous gain of massive MIMO and yet reduce its cost to an affordable level, this paper proposes a novel system design by integrating an electromagnetic (EM) lens with the large antenna array, termed \emph{electromagnetic lens antenna} (ELA). An ELA has the capability of focusing the power of any incident plane wave passing through the EM lens to a small subset of the antenna array, while the location of focal area is dependent on the angle of arrival (AoA) of the wave. As compared to conventional antenna arrays without the EM lens, the proposed system can substantially reduce the number of required radio frequency (RF) chains at the receiver and hence, the implementation costs. In this paper, we investigate the proposed system under a simplified single-user uplink transmission setup, by characterizing the power distribution of the ELA as well as the resulting channel model. Furthermore, by assuming antenna selection used at the receiver, we show the throughput gains of the proposed system over conventional antenna arrays given the same number of selected antennas.