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We study and analyze the electric dipole moments (EDMs) of neutron and heavyquarks c, t in a CP-violating (CPV) supersymmetric U(1) extension of thestandard model called $U(1)_X$SSM, whose local gauge group is $U(1)_X\timesSU(3)_C\times SU(2)_L \times U(1)_Y$. The contributions from the one loopdiagrams and the Weinberg operators are taken into account with the newintroduced CPV phases beyond the minimum supersymmetric standard model(MSSM)being non-zero. Our numerical results show that in $U(1)_X$SSM the neutron EDMcan be smaller than its experimental upper bound $1.8\times10^{-26}$ e$\cdot$cmwithout a small CPV phase. The magnitudes of EDMs of heavy quarks c and t canreach $10^{-24}$ e$\cdot$cm. and $10^{-22}$ e$\cdot$cm respectively. This isfavorable to the study of CPV.

Electric dipole moments of neutron and heavy quarks c, t in CP violating $U(1)_X$SSM