The present invention provides a modified conjugated diene polymer that is prepared by polymerization of a conjugated diene compound using a catalyst containing a lanthanoid rare earth element compound in an organic solvent and then modifying the resulting polymer having an active organic metal site with a modifier, wherein the modification efficiency is not less than 15% and the cis-1,4 bond content in the conjugated diene moiety measured by Fourier transform infrared spectroscopy satisfies the relationship (I):
cis-1,4 bond content≧98.00(%) (I),
or the modification efficiency is not less than 75% and the cis-1,4 bond content in the conjugated diene moiety measured by Fourier transform infrared spectroscopy satisfies the relationship (II):
94.00(%)≦cis-1,4 bond content<98.00(%) (II).
The invention further provides a rubber composition containing the modified conjugated diene polymer and giving a tire exhibiting low heat build-up, satisfactory failure characteristics, and high abrasion resistance, and a tire composed of the rubber composition and exhibiting these characteristics.