Multiblock copolymers 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 full of challenge. We reported here a ternary catalyst of Nd(CF3SO3)3·H2O·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, WAXD, and DSC. Finally, the chain shuttling mechanism is confirmed through 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.