The theoretical temperature-concentration-electric field (T-x-E) phase diagram of (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) is investigated under the electric fields applied along the [001], [011] and [111] directions in the pseudo-cubic coordinate. Using the structurally stable tenth-order Landau–Ginzburg–Devonshire potential model, different two-dimensional sections of T-x-E phase diagram such as T-x (E[001] = E[101] = 0.1, 1kV/㎝) and E-T (x = 0.26, 0.28, 0.3, 0.32, 0.34, 0.36 and 0.38) phase diagrams, and T-x-E[001] one are constructed for PMN-PT single crystals. Also, based on the phenomenological results for T-x-E phase diagram, the features of symmetry changes from high symmetry phase, cubic one, to low symmetry phases, rhombohedral, tetragonal, orthorhombic, monoclinic and triclinic ones, possible during the phase transitions occurring at different temperatures, concentrations and electric fields in PMN-PT single crystals are predicted. The anomalies in dielectric and piezoelectric coefficients accompanied with the symmetry changes are studied. The topological features of T-x-E phase diagram of PMN-PT single crystals are qualitatively in good agreement with those of different piezo/ferroelectrics (BaTiO3, KNbO3, (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT)) in which the symmetry of order parameter is characterized by the image-group ImΓ4− = m3m of the irreducible representation Γ4− of the space group Pm3‾m as in PMN-PT single crystals.