A pneumatic radial tire, wherein: in a cross sectional view in the tire widthwise direction thereof in a state where the tire is assembled with an application rim, inflated at a predetermined air pressure and mounted on a vehicle under a predetermined load exerted thereon, there is: a first imaginary line, passing through the maximum width position remotest from the tire equatorial plane in a tire side portion situated on the vehicle outer side, to extend to be orthogonal to the tire equatorial plane; and a second imaginary line, passing through the maximum width position remotest from the tire equatorial plane in a tire side portion situated on the vehicle inner side, to extend to be orthogonal to the tire equatorial plane; and provided that: H out represents a distance in the tire radial direction between the first imaginary line and a ground-contact end on the vehicle outer side of the tread; and H in represents a distance in the tire radial direction between the second imaginary line and a ground-contact end on the vehicle inner side of the tread, H out < H in; radius of curvature (R out) of the tire side portion on the vehicle outer side, at the maximum width position thereof, is smaller than radius of curvature (R in) of the tire side portion on the vehicle inner side, at the maximum width position thereof; characterized in that: a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle outer side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle is smaller than a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle inner side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle; and an outer end in the tire radial direction of a turn-up portion around a bead core, of a carcass constituted of at least of one carcass ply, is disposed in each of the half portions of the tire at a height in the tire radial direction of at least 40% of the tire cross sectional height under no load exerted on the tire. in a cross sectional view in the tire widthwise direction thereof in a state where the tire is assembled with an application rim, inflated at a predetermined air pressure and mounted on a vehicle under a predetermined load exerted thereon, there is: a first imaginary line, passing through the maximum width position remotest from the tire equatorial plane in a tire side portion situated on the vehicle outer side, to extend to be orthogonal to the tire equatorial plane; and a second imaginary line, passing through the maximum width position remotest from the tire equatorial plane in a tire side portion situated on the vehicle inner side, to extend to be orthogonal to the tire equatorial plane; and provided that: H out represents a distance in the tire radial direction between the first imaginary line and a ground-contact end on the vehicle outer side of the tread; and H in represents a distance in the tire radial direction between the second imaginary line and a ground-contact end on the vehicle inner side of the tread, H out < H in; radius of curvature (R out) of the tire side portion on the vehicle outer side, at the maximum width position thereof, is smaller than radius of curvature (R in) of the tire side portion on the vehicle inner side, at the maximum width position thereof; characterized in that: a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle outer side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle is smaller than a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle inner side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle; and an outer end in the tire radial direction of a turn-up portion around a bead core, of a carcass constituted of at least of one carcass ply, is disposed in each of the half portions of the tire at a height in the tire radial direction of at least 40% of the tire cross sectional height under no load exerted on the tire. a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle outer side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle is smaller than a negative ratio of a ground-contact surface of the tread of a half portion, on the vehicle inner side with respect to the tire equatorial plane, of the tire when the tire is mounted on the vehicle; and an outer end in the tire radial direction of a turn-up portion around a bead core, of a carcass constituted of at least of one carcass ply, is disposed in each of the half portions of the tire at a height in the tire radial direction of at least 40% of the tire cross sectional height under no load exerted on the tire.