Massive multiple-input multiple-output (MIMO) is one of the promising technologies to be used in the future fifth generation (5G) wireless networks for its capability to increase the system throughput, improve spectral efficiency and energy efficiency. To achieve these benefits of the massive MIMO, there are many challenges that need to be handled. One of these challenges is the pilot contamination problem that arises from reusing pilot sequences among the system cells. Since this problem is considered as a bottleneck of the system performance, it attracted many researchers who proposed schemes to solve it. In this paper, we propose a new scheme that mitigates its effect by adopting both asynchronous pilot transmission (APT) and fractional pilot reuse (FPR). We compare the performance of our proposed scheme with other schemes using computer simulations and show that our proposed scheme enhances the performance of the time division duplex (TDD) multi-cell massive MIMO systems in terms of the signal to interference and noise ratio (SINR) and capacity.