Parity time symmetry breaking was obtained in a specially designed fiber ring laser with a homemade tunable isolator in the cavity. The dynamic evolution of the cavity eigenmodes around the exceptional point (EP) was further experimentally studied. We showed that operating the laser near the EP can facilitate single longitudinal mode lasing. A single-frequency fiber laser with a linewidth of 163 Hz was first, to the best of our knowledge, demonstrated near the EP of the cavity without using any filter with a narrow bandwidth.