The present invention relates to a method for preparing neodymium-carbon-nanotube and a process for preparing 1,4-cis-polybutadiene utilizing the same and more particularly, neodymium-carbon-nanotube. Neodymium is introduced by coordination with carboxylic acid, which is formed on the surface of carbon nanotube. In 1,3-butadiene polymerization with the neodymium-catalyst comprising the neodymium-carbon nanotube, a particular halogen compound, and a particular organometallic compound in an appropriate ratio, high 1,4-cis polybutadiene having molecular weight of 10,000 to 2,000,000 is produced, which exhibits excellent mechanical properties such as elasticity and durability.