The shapes of zirconium isotopes remain an unsettled question drawing many interests. Recent analysis based on the STAR measurement in relativistic heavy-ion collision experiments provide evidences of non-zero β 30 in the ground state of 96 Zr [1], however, conventional nuclear structure models do not favour these pear-like shapes. To resolve this issue, in this work we perform systematic projection-after-variation calculations for 96 Zr based on the multidimensionally constrained relativistic Hartree-Bogoliubov model. We consider all β λµ with even µ simultaneously and present selected potential energy surfaces (PES's) and projected PES's with certain angular momentum and parity combinations. While the mean-field calculations always predict reflection-symmetric ground states, static octupole deformations emerge after projecting to the 0 + state. We find that β 20 , β 22 , β 30 and β 32 are all necessary for describing the ground state and their values vary significantly for excited states with different angular momenta and parities. These complex structures originate from the competition among various shell structures in this mass region. Our results suggest that both beyond-mean-field effects and exotic shapes are essential elements for understanding the structure of 96 Zr.