The dielectric properties of Pb(Zn1/3Nb2/3) O3-PbZrO3−PbTiO3 (PZN-PZ-PT) system near the rhombohedral/tetragonal morphotropic phase boundary (MPB) are carefully studied in this paper. It is found that, for all samples, the curves around the temperatures of dielectric permittivity peak show the characteristics of diffuse phase transition. The change in PbZrO3/PbTiO3 ratio has much influence on the dielectric properties of the samples. The extent of diffuse phase transition increases with the increasing Zr/Ti ratio. The samples in rhombohedral region have typical diffuse phase transition in the temperature range measured. However, for the samples with tetragonal symmetry, a spontaneous normal ferroelectric-relaxor phase transition exists at temperature lower than that of permittivity peak. This normal ferroelectric-relaxor phase transition is confirmed by the experiment of thermally driven current. The analysis of TEM reveals that the samples in tetragonal region show a 90% macrodomain structure, while the samples in rhombohedral region have the configuration of microdomain structure.