A rubber composition for tire treads is disclosed which is designed to exhibit high resistance to skidding on wet, icy and snowy roads. A selected rubber blend of styrene-butadiene rubber and natural rubber and/or polyisoprene rubber is combined with a selected carbon black of specified specific surface areas and also with a selected softener of specified viscosity-gravity constants. The styrene-butadiene rubber consists essentially of two styrene-butadiene block copolymers each having varied styrene and vinyl contents and a specified transition temperature width, one block having a higher glass transition temperature than the other.