  By introducing the next-nearest-neighboring (NNN) intersite coupling, we
investigate the eigenenergies of the $\cal PT$-symmetric non-Hermitian
Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials at
the end sites. It is found that with the strengthening of NNN coupling, the
particle-hole symmetry is destroyed. As a result, the bonding band is first
narrowed and then undergoes the top-bottom reversal followed by the its width's
increase, whereas the antibonding band is widened monotonously. In this
process, the topological state extends into the topologically-trivial region,
and its energy departs from the energy zero point, accompanied by the emergence
of one new topological state in this region. All these results give rise to the
complication of the topological properties and the manner of $\cal PT$-symmetry
breaking. It can be concluded that the NNN coupling takes important effects to
the change of the topological properties of the non-Hermitian SSH system.
