Massive multiple-input multiple-output (MIMO) has been extensively studied and considered as a key enabling technology for the fifth generation (5G) wireless communication systems, due to its potential to achieve high energy efficiency and spectral efficiency. As the concept of massive MIMO becomes more popular, it is plausible that the eavesdroppers will also employ massive antennas, which may remarkably enhance their ability to intercept the information. In this paper, motivated by the need to protect against the eavesdroppers equipped with powerful large antenna arrays, which has received scarce attention in the literature, a physical layer security approach called original symbol phase rotated (OSPR) secure transmission scheme is proposed to defend against eavesdroppers armed with unlimited antennas. The basic idea of the proposed OSPR scheme is to randomly rotate the phase of original symbols at the base station (BS) before they are transmitted, so that the massive MIMO eavesdropper will be confused by the intercepted signals, which may not represent the true information symbols. However, the legitimate users are able to infer the correct phase rotations and take proper inverse operations to recover the original symbols. We show that when the BS has a large enough, but finite number of antennas, the proposed OSPR scheme can achieve a considerable security performance in that the eavesdropper is unable to recover most of the original symbols, even with unlimited antennas. The process and the security performance of the proposed OSPR scheme are presented in detail. Simulation results are provided to further corroborate that the proposed OSPR scheme is a potential green secure transmission candidate technique for the future wireless networks.