An anti-vibration wheel for an automobile, comprising: a disk member connectable to an axle hub with a rim member extending from a circumferential edge of the disk member for mounting a tire, the rim member further having: an outer bead seat positioned at an outer end of the rim member where an outer bead of the tire sits, an inner bead seat positioned at an inner end of the rim member where an inner bead of the tire sits, and a wheel portion which is inclined and extends between the outer bead seat and the inner bead seat, with an outer wheel portion extending from the outer bead seat and an inner wheel portion extending from the outer wheel portion, with the thickness of the outer wheel portion being greater than the thickness of the inner bead seat which is greater than the thickness of the inner wheel portion, characterized in that the anti-vibration wheel further comprises: an outside cap attachably/detachably connected to an outside surface of a spoke portion connecting a hub mounting portion of the disk member connected to the axle hub and the rim member; and an outside vibration damping plate provided to the outside cap to be in contact with the spoke portion, to dampen vibration and wherein the outside vibration damping plate is formed such that the thickness gradually increases from one end to the other end, where one end is thicker relative to the opposite end which is thinner, and the outside vibration damping plate is positioned such that the thicker end is positioned towards the rim member and the thinner end is positioned towards the hub mounting portion. a disk member connectable to an axle hub with a rim member extending from a circumferential edge of the disk member for mounting a tire, the rim member further having: an outer bead seat positioned at an outer end of the rim member where an outer bead of the tire sits, an inner bead seat positioned at an inner end of the rim member where an inner bead of the tire sits, and a wheel portion which is inclined and extends between the outer bead seat and the inner bead seat, with an outer wheel portion extending from the outer bead seat and an inner wheel portion extending from the outer wheel portion, with the thickness of the outer wheel portion being greater than the thickness of the inner bead seat which is greater than the thickness of the inner wheel portion, characterized in that the anti-vibration wheel further comprises: an outside cap attachably/detachably connected to an outside surface of a spoke portion connecting a hub mounting portion of the disk member connected to the axle hub and the rim member; and an outside vibration damping plate provided to the outside cap to be in contact with the spoke portion, to dampen vibration and wherein the outside vibration damping plate is formed such that the thickness gradually increases from one end to the other end, where one end is thicker relative to the opposite end which is thinner, and the outside vibration damping plate is positioned such that the thicker end is positioned towards the rim member and the thinner end is positioned towards the hub mounting portion. an outer bead seat positioned at an outer end of the rim member where an outer bead of the tire sits, an inner bead seat positioned at an inner end of the rim member where an inner bead of the tire sits, and a wheel portion which is inclined and extends between the outer bead seat and the inner bead seat, with an outer wheel portion extending from the outer bead seat and an inner wheel portion extending from the outer wheel portion, with the thickness of the outer wheel portion being greater than the thickness of the inner bead seat which is greater than the thickness of the inner wheel portion, characterized in that the anti-vibration wheel further comprises: an outside cap attachably/detachably connected to an outside surface of a spoke portion connecting a hub mounting portion of the disk member connected to the axle hub and the rim member; and an outside vibration damping plate provided to the outside cap to be in contact with the spoke portion, to dampen vibration and wherein the outside vibration damping plate is formed such that the thickness gradually increases from one end to the other end, where one end is thicker relative to the opposite end which is thinner, and the outside vibration damping plate is positioned such that the thicker end is positioned towards the rim member and the thinner end is positioned towards the hub mounting portion. an outside cap attachably/detachably connected to an outside surface of a spoke portion connecting a hub mounting portion of the disk member connected to the axle hub and the rim member; and an outside vibration damping plate provided to the outside cap to be in contact with the spoke portion, to dampen vibration and wherein the outside vibration damping plate is formed such that the thickness gradually increases from one end to the other end, where one end is thicker relative to the opposite end which is thinner, and the outside vibration damping plate is positioned such that the thicker end is positioned towards the rim member and the thinner end is positioned towards the hub mounting portion.