  In this paper, a one-dimensional non-Hermitian quasiperiodic $p$-wave
superconductor without $\mathcal{PT}$-symmetry is studied. By analyzing the
spectrum, we discovered there still exists real-complex energy transition even
if the inexistence of $\mathcal{PT}$-symmetry breaking. By the inverse
participation ratio, we constructed such a correspondence that pure real
energies correspond to the extended states and complex energies correspond to
the localized states, and this correspondence is precise and effective to
detect the mobility edges. After investigating the topological properties, we
arrive at a fact that the Majorana zero modes in this system are immune to the
non-Hermiticity.
