The phase transition and dielectric properties of Pb-0.988(Hf0.945SnxTi0.03-xNb0.025)O-3 ceramics (0 <= x <= 0.03, correspondingly abbreviated as H1, H2, H3, and H4) at the morphotropic phase boundary were systematically investigated. X-ray diffraction results and P-E hysteresis loops show that the dominate orthorhombic antiferroelectric phase and a small amount of the tetragonal FE phase coexist in Pb-0.988(Hf0.945SnxTi0.03-xNb0.025)O-3 ceramics. As the Sn content increases, the antiferroelectricity is significantly enhanced, accompanied with an increased Curie temperature and sharply reduced peak dielectric constant. H1 and H2 experience an irreversible field-induced AFE-FE phase transition at the ambient temperature, and the transition from a metastable FE phase to the original AFE phase is observed in H2 when heated to 60 degrees C. H3 and H4 experience an invertible AFE-FE phase transition, along with an enhanced forward phase switching field E-F. Moreover a decreased backward phase switching field E-A for H4 is detected as the electric field increases due to the AFE/FE coexistence. These results reveal the unique phase transition characteristics of AFE materials near the phase boundary, which is helpful for better understanding of AFE/FE materials.