Recent researches on disorder-driven many-body localization (MBL) in non-Hermitian quantum systems have aroused great interest. In this work, we investigate the non-Hermitian MBL in a one-dimensional hard-core Bose model induced by random two-body dissipation, which is described by

　　　　　　　　　　　 \hatH=\displaystyle\sum\limits_j^L-1\left -J\left( \hatb_j^\dagger\hatb_j+1+\hat b_j+1^\dagger\hatb_j\right) +\frac12\left( U-\mathrmi\gamma_j\right) \hatn_j\hatn_j+1\right \notag,

with the random two-body loss \gamma_j\in\left0,W\right. By the level statistics, the system undergoes a transition from the AI^\dagger symmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength. This transition is accompanied by the changing of the average magnitude (argument) \overline\left\langle r\right\rangle (\overline-\left\langle \cos \theta\right\rangle ) of the complex spacing ratio, shifting from approximately 0.722 (0.193) to about 2/3 (0). The normalized participation ratios of the majority of eigenstates exhibit finite values in the ergodic phase, gradually approaching zero in the non-Hermitian MBL phase, which quantifies the degree of localization for the eigenstates. For weak disorder, one can see that average half-chain entanglement entropy \overline\langle S \rangle follows a volume law in the ergodic phase. However, it decreases to a constant independent of L in the deep non-Hermitian MBL phase, adhering to an area law. These results indicate that the ergodic phase and non-Hermitian MBL phase can be distinguished by the half-chain entanglement entropy, even in non-Hermitian system, which is similar to the scenario in Hermitian system. Finally, for a short time, the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder. In strong disorder case, the short-time evolution of \overlineS(t) shows logarithmic growth. However, when t\geqslant10^2, \overlineS(t) can stabilize and tend to the steady-state half-chain entanglement entropy \overline S_0 . The results of the dynamical evolution of \overlineS(t) imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of \overlineS(t), and the long-time behavior of \overlineS(t) signifies the steady-state information.