Structural and dielectric characterizations of the relaxor ferroelectric PbZn1/3Nb2/3 (PZN) were carried out on single crystals in the temperature range of the dielectric anomaly (370 K andlt; T andlt; 440 K), under dc electric field applied along [001]- and [111]-directions. Two ferroelectric phases, tetragonal (T) and rhombohedral (R), can be field induced in this temperature range, the symmetry of which depends on the direction of the applied field. [001] and [111] respectively. E-T diagrams were built and interpreted under the consideration of polar nano-regions (PNRs) with a prominent tetragonal component. These PNRs prevent the onset of a monodomain state when the field is applied along [111] and explain the features of PZN for an applied field along [001] large lattice strain, easy onset of the T phase and suppression of the dielectric relaxation for E ≥ 1.5 kV cm-1. The microscopic origin of these PNRs can be discussed in relation with recent nuclear magnetic resonance and structural results reported in other isomorphous relaxors.