Massive multiple-input multiple-output (MIMO) is considered as a promising technique in wireless communication systems, which contains cellular base stations equipped with a very large number of antennas to serve multiple users. However, the performance of massive MIMO is limited by the impact of pilot contamination due to inter-cell interference (ICI). In conventional massive MIMO systems, pilot sequences are randomly assigned to users without any further consideration. In this paper, a vertex graph coloring-based pilot assignment (VGC-PA) algorithm is proposed in conjunction with the existing post-processing discrete Fourier transform (DFT) filtering channel estimation to mitigate the ICI between users with the same pilot sequence in the channel estimation process to improve the capacity of the whole system. Specifically, we propose a metric to measure the potential ICI strength between any two users in the system based on their angle of arrival, correlation, and distances to construct an ICI graph, where each user is regarded as a node. This ICI graph denotes the potential ICI strength relationship among all users in the system. Then, we propose a VGC-PA algorithm to mitigate the ICI relationship between users with the same pilot sequences by assigning different pilots to connected users with high ICI metric based on some criteria. After the pilot assignment process, we apply the existing post-processing DFT filtering in the channel estimation process. The simulation results show the significant improvement of our proposed VGC-PA algorithm compared with existing methods.