A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe two-flavor normal quark matter. Depending on whether m₀/Λ, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be of the second or first order. A complete phase diagram of u quark chemical potential versus m₀ is given. With the electrical neutrality constraint, the region where the second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value of m₀/Λ from QCD phenomenology, the phase transition must be of the first order.