  The potential energy surfaces of even-even $^{142-156}$Ba are investigated in
the constrained reflection-asymmetric relativistic mean-field approach with
parameter set PK1. It is shown that for the ground states, $^{142}$Ba is near
spherical,$^{156}$Ba well quadrupole-deformed, and in between $^{144-154}$Ba
octupole deformed. In particular, the nuclei $^{148,150}$Ba with $N=92,94$ have
the largest octupole deformations. By including the octupole degree of freedom,
energy gaps $N=88$, $N=94$ and $Z=56$ near Fermi surfaces for the
single-particle levels in $^{148}$Ba with $\beta_2\sim 0.26$ and $\beta_3\sim
0.17$ are found. Furthermore, the performance of the octupole deformation
driving pairs ($\nu 2f_{7/2}$, $\nu 1i_{13/2}$) and ($\pi 2d_{5/2}$, $\pi
1h_{11/2}$) is demonstrated by analyzing the single-particle levels near Fermi
surfaces in $^{148}$Ba.
