The issue of the existence of reflection asymmetry in $^{145}\mathrm{Ba}$ has stood for the past 30 years without a common conclusion. The recent experimental data show a number of low-lying rotational bands with alternative parities, providing more strict constraints on the relevant modeling. With a proper octupole deformation, all the observed six rotational bands in $^{145}\mathrm{Ba}$ have been well reproduced by the reflection asymmetric shell model (RASM). The three octupole deformed neutron single-particle orbitals just above the octupole shell gap 88, with $K=1/2,K=3/2$, and $K=5/2$, respectively, dominate the intrinsic configurations of the observed bands. Based on the analysis of the calculated RASM wave functions, the assignments for the observed bands have been given. The experimental yrast band ($\ensuremath{\Delta}I=1$) presents a simplex inversion at around the $11/{2}^{\ensuremath{-}}$ state where the simplex staggering phase changes. This phenomenon may be explained in the framework of the RASM as from the change of the dominate intrinsic configuration, induced by the band mixing. The present results strongly support the appearance of the reflection asymmetry in the ground and low-lying states of $^{145}\mathrm{Ba}$.