The structure and dielectric properties of poled <001>-oriented 0.7Pb($Mg_{1/3}Nb_{2/3})O_3-0.3PbTiO_3$ (PMN-0.3PT) crystals have been investigated for orientations both parallel and perpendicular to the [001] poling direction. An electric field induced monoclinic phase was observed for the initial poled sample. The phase remained stable after the field was removed. A quite different temperature dependence of dielectric constant has been observed between heating and cooling due to an irreversible phase transformation. The results of mesh scans and temperature dependence of the dielectric constant demonstrate that the initial monoclinic phase changes to a single domain tetragonal phase at 370K and to a paraelectric cubic phase at 405K upon heating. However, upon subsequent cooling from the unpoled state, the cubic phase changes to a poly domain tetragonal phase and to a rhombohedral phase. In the ferroelectric tetragonal phase with a single domain state, the dielectric constant measured perpendicular to the poling direction was dramatically higher than that of the parallel direction. A large dielectric constant implies easier polarization rotation away from the polar axis. This enhancement is believed to be related to dielectric softening close to the morphotropic phase boundary and at the phase transition temperature.