We investigate the effect of the electric-charge neutrality in $beta$ equilibrium on the chiral phase transition by solving the chiral and diquark condensates in the two-flavor Nambu--Jona-Lasinio model. We demonstrate that the electric-charge neutrality plays a similar role as the repulsive vector interaction; they both weaken the first-order chiral phase transition in the high-density and low-temperature region. The first-order chiral phase transition is not affected, however, at finite temperatures where the diquark condensate melts. In this way the chiral phase transition could be second-order at intermediate temperatures if the diquark effects overwhelm the chiral dynamics, while the first-order transition may survive at lower and higher temperatures. The number of the critical points appearing on the phase diagram can vary from zero to three, which depends on the relative strength of the chiral and diquark couplings. We systematically study the possibility of the phase structure with multiple QCD critical points and evaluate the Meissner screening mass to confirm that our conclusion is not overturned by chromomagnetic instability.
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