Geometries and energy separations of several electronic states of Zr4 are computed using the complete-active space self-consistent field technique followed by multi-references singles+doubles configuration interaction which included up to 3.3 million configurations. We find two nearly degenerate states, namely, 1A(g) and 3B1u of rhombus equilibrium geometries. Our computed Zr-Zr side bond lengths are 2.79 and 2.81 A while the bond angles are 62-degrees and 63-degrees, respectively, for these two states.