  The searching for the electric dipole moments (EDMs) of neutron ($d_n$), $b$
quark ($d_b$) and $c$ quark ($d_c$) gives strict upper bounds on these
quantities. And recently, new upper bounds on $d_b$, $d_c$ are obtained by the
strict limit on $d_n$. The models of new physics (NP) with additional
CP-violating (CPV) sources are constrained strictly by these EDMs. In this
work, we focus on the CPV effects on these EDMs in the minimal supersymmetric
extension (MSSM) of the SM with local $B-L$ gauge symmetry (B-LSSM). The
contributions from one-loop and some two-loop diagrams to the quark EDM are
given in general form, which can also be used in the calculation of quark EDM
in other models of NP. Considering the constrains from updated experimental
data, the numerical results show that the two-loop corrections can make
important contributions to these EDMs. Compared with the MSSM, the effects of
new CPV phases and new parameters in the B-LSSM on these EDMs are also
explored.
