Multiblock copolymer's of cis-1,4- and trans-1,4-polybutadiene (PBD) have shown exciting and unique elastic properties: But the catalyst that can steadily regulate the:Content and the distribution,of the stereoselective monomers in the PBD copolymer is fa of challenge. We reported here a ternary catalyst of Nd(CF3SO3)(3)center dot H2O center dot 3TBP/Mg(n-Bu)(2)/MMAO (TBP: tributyl phosphate; MMAO: modified methylaluminoxane) that can synthesize such copolymer via chain shuttling polymerization in a highly efficient and tunable way. The stereoselectivity of the cis-1,4 and trans-1,4 monomers in the PBD copolymers can be well regulated through the [MMAO]/[Nd] ratio, the [Mg]/[Nd] ratio, and the delayed feeding time of MMAO. The increase of the [MMAO]/[Nd] ratio and the delayed feeding time of MMAO as well as the reduced [Mg]/[Nd] ratio all result in the increase of the trans-1,4 content in the product from 8.4% to 95.3%. The multiblock rather than the diblock structure for the copolymer is validated by NMR, WARD, and DSC. Finally, the chain Shuttling mechanism is confirmed thtough the self-consistence in the relationship between the composition of the catalyst and the cis-1,4 and trans-1,4 contents in the PBD copolymer.