Rubber polymer, method for preparing thereof, and rubber composition comprising the same

A method of preparing a rubber polymer, comprising the steps of:

• (a) allowing a conjugated diene-based monomer to react in the presence of a catalyst;
• and
• (b) allowing the product of the step (a) to react with at least one of compounds represented by the following Chemical Formula 4:
• in Chemical Formula,
• B is oxygen or sulfur,
• C is silicon or tin,
• Z is a functional group represented by the following Chemical Formula Z,
• each R2 is independently a C1 to C20 linear or branched substituted or unsubstituted alkyl group, a C3 to C20 substituted or unsubstituted cycloalkyl group, or a C6 to C20 substituted or unsubstituted aryl group,
• wherein:
• the rubber polymer is prepared by using a polymerization system including a neodymium-based catalyst,
• the rubber polymer has a degree of branching of 2.0 to 2.5,
• the rubber polymer has a molecular weight distribution (Mw/Mn) of 1.5 to 2.5, and
• the degree of branching is calculated by the ratio of the Mooney viscosity (MV) and solution viscosity (SV) at 25° C., multiplied by 10(MV/SV*10).