It was proposed that large dielectric constants in Pb(Zn1/3Nb2/3)O3–xPbTiO3 (PZN–xPT) crystals are mainly due to the fluctuation of polarization along the spherical direction (perpendicular to the spontaneous polarization) near the morphotropic phase boundary (MPB), named transversal instability [M. Iwata and Y. Ishibashi: in Ferroelectric Thin Films, ed. M. Okuyama and Y. Ishibashi (Springer, 2005) Part III, p. 127]. The dielectric anisotropy in the MPB region of PZN–xPT was investigated to clarify the origin of the large dielectric constant in perovskite-type relaxors. It was found that the dielectric constant perpendicular to the spontaneous polarization indicating transversal instability markedly increases as it approaches MPB. The dielectric anisotropy and large dielectric constant near the MPB were discussed in terms of the phenomenological theory.