A vane compressor comprising: - a cylinder including a cylindrical inner circumferential surface that defines a hole having opposite openings; - a cylinder head that covers one of the openings; - a frame that covers another one of the openings; - a cylindrical rotor portion configured to rotate about a rotation axis displaced from a central axis of the inner circumferential surface inside the cylinder; - a rotating shaft portion configured to transmit a rotational force to the rotor portion; and - a vane (5a, 6a) disposed inside the rotor portion, held rotatably about a center of the cylinder inner circumferential surface of the cylinder, and partitioning a compression space formed between the cylinder and the rotor portion into at least a suction space and a discharge space; - wherein each of the frame and the cylinder head includes a recess (2a, 3a) or a ring-shaped groove in an end face near the cylinder, the recess (2a, 3a) or the ring-shaped groove having an outer circumferential surface concentric with the inner circumferential surface of the cylinder, characterised in that - a vane aligner (5c, 5d, 6c, 6d) having a partial ring-shape and configured to support the vane (5a, 6a) is provided, the vane aligner (5c, 5d, 6c, 6d) being capable of freely sliding and rotating along the outer circumferential surface, and integrally attached to the vane (5a, 6a) or integrally formed with the vane (5a, 6a) so as to keep a gap between a tip of the vane (5a, 6a) and the inner circumferential surface of the cylinder, - a first discharge port communicating with the compression space and a second discharge port (1e, 1g, 2f) communicating with the compression space are provided, the first discharge port configured to allow a gas compressed in the compression space to be discharged therethrough, the second discharge port (1e, 1g, 2f) being provided at a location upstream from the first discharge port in a compression stroke, and - wherein the second discharge port (1e, 1g, 2f) includes an opening portion to the compression space, the opening portion having a width equal to or smaller than the width of the vane (5a, 6a), - wherein the vane (5a, 6a) is supported such that the vane (5a, 6a) is capable of rotating and sliding with respect to the rotor portion, and - wherein the tip of the vane (5a, 6a) has an outwardly curved arc shape, and the arc shape has a radius substantially equal to the radius of the inner circumferential surface of the cylinder while the line normal to the arc shape of the vane tip (5b, 6b) and the line normal to the cylinder inner circumferential surface continuously coincide with each other. - a cylinder including a cylindrical inner circumferential surface that defines a hole having opposite openings; - a cylinder head that covers one of the openings; - a frame that covers another one of the openings; - a cylindrical rotor portion configured to rotate about a rotation axis displaced from a central axis of the inner circumferential surface inside the cylinder; - a rotating shaft portion configured to transmit a rotational force to the rotor portion; and - a vane (5a, 6a) disposed inside the rotor portion, held rotatably about a center of the cylinder inner circumferential surface of the cylinder, and partitioning a compression space formed between the cylinder and the rotor portion into at least a suction space and a discharge space; - wherein each of the frame and the cylinder head includes a recess (2a, 3a) or a ring-shaped groove in an end face near the cylinder, the recess (2a, 3a) or the ring-shaped groove having an outer circumferential surface concentric with the inner circumferential surface of the cylinder, - a vane aligner (5c, 5d, 6c, 6d) having a partial ring-shape and configured to support the vane (5a, 6a) is provided, the vane aligner (5c, 5d, 6c, 6d) being capable of freely sliding and rotating along the outer circumferential surface, and integrally attached to the vane (5a, 6a) or integrally formed with the vane (5a, 6a) so as to keep a gap between a tip of the vane (5a, 6a) and the inner circumferential surface of the cylinder, - a first discharge port communicating with the compression space and a second discharge port (1e, 1g, 2f) communicating with the compression space are provided, the first discharge port configured to allow a gas compressed in the compression space to be discharged therethrough, the second discharge port (1e, 1g, 2f) being provided at a location upstream from the first discharge port in a compression stroke, and - wherein the second discharge port (1e, 1g, 2f) includes an opening portion to the compression space, the opening portion having a width equal to or smaller than the width of the vane (5a, 6a), - wherein the vane (5a, 6a) is supported such that the vane (5a, 6a) is capable of rotating and sliding with respect to the rotor portion, and - wherein the tip of the vane (5a, 6a) has an outwardly curved arc shape, and the arc shape has a radius substantially equal to the radius of the inner circumferential surface of the cylinder while the line normal to the arc shape of the vane tip (5b, 6b) and the line normal to the cylinder inner circumferential surface continuously coincide with each other.