Tire rubber composition and pneumatic tire

The present invention provides a tire rubber composition with which the grip performance, the abrasion resistance, and the performance in terms of rolling resistance are improved in a balanced manner. The present invention relates to a tire rubber composition comprising: a modified diene rubber A which is modified with a specific acrylamide compound; and a modified diene rubber B which is modified with a specific modifying compound alone or together with a specific silicon or tin compound, a weight average molecular weight of a total of the modified diene rubbers A and B being 300,000 to 1,400,000.