A compressor, comprising: a driving motor ; a rotational shaft configured to transmit a rotational force of the driving motor; a cylinder installed at one side of the driving motor and having a radius (A); a roller having an outer circumferential surface having an elliptical shape contacting an inner circumferential surface of the cylinder, rotated by being provided at the rotational shaft, and concentric with the cylinder, wherein the roller has a rotational center (O), a long-axis radius (A) and a short-axis radius (B); and two vanes movably provided at the cylinder, contacting an outer circumferential surface of the roller, and configured to divide two compression spaces formed by the cylinder and the roller into a suction chamber and a compression chamber (V, V1, V2), characterized in that the roller is provided on the outer circumferential surface with an increased portion , a decreased portion as a lubrication surface, and a connection portion where the connection portion is formed to have a curved surface having a common tangent is formed between the increased portion and the decreased portion , wherein a distance from the rotation center (O) to the outer circumferential surface of the increased portions is gradually increased towards the decreased portions; and wherein the lubrication surface on its outer circumferential surface contacting in surface-contact with the inner circumferential surface of the cylinder, the lubrication surface having a radius A' from a rotation center (O) of the roller, wherein A ′ = A 2 B 2 cos 2 D A 2 tan 2 D + B 2 , and wherein (D) is a half circumferential angle of the roller . a driving motor ; a rotational shaft configured to transmit a rotational force of the driving motor; a cylinder installed at one side of the driving motor and having a radius (A); a roller having an outer circumferential surface having an elliptical shape contacting an inner circumferential surface of the cylinder, rotated by being provided at the rotational shaft, and concentric with the cylinder, wherein the roller has a rotational center (O), a long-axis radius (A) and a short-axis radius (B); and two vanes movably provided at the cylinder, contacting an outer circumferential surface of the roller, and configured to divide two compression spaces formed by the cylinder and the roller into a suction chamber and a compression chamber (V, V1, V2), characterized in that the roller is provided on the outer circumferential surface with an increased portion , a decreased portion as a lubrication surface, and a connection portion where the connection portion is formed to have a curved surface having a common tangent is formed between the increased portion and the decreased portion , wherein a distance from the rotation center (O) to the outer circumferential surface of the increased portions is gradually increased towards the decreased portions; and wherein the lubrication surface on its outer circumferential surface contacting in surface-contact with the inner circumferential surface of the cylinder, the lubrication surface having a radius A' from a rotation center (O) of the roller, wherein A ′ = A 2 B 2 cos 2 D A 2 tan 2 D + B 2 , and wherein (D) is a half circumferential angle of the roller . <EOS>