There are provided a rubber composition simultaneously improving low loss factor and wear resistance as compared with the conventional ones as well as a tire using such a rubber composition.The invention lies in a rubber composition using a modified conjugated diene rubber and being excellent in the low loss factor and wear resistance as well as a tire. The rubber composition of the invention is formed by compounding a filler to a rubber component containing (A) a modified conjugated diene rubber having a cis-bond content in conjugated diene portion of not less than 87% and a vinyl bond content of not more than 2% and containing a functional group reactive with a filler and (B) a modified polymer having a modifying functional group number per 1 molecule of an unmodified polymer of not less than 0.6.