A cutting insert formed of a plate-like member with a substantially polygonal outer shape and comprising: a rake face with a chip breaker which is formed on at least one of top and bottom surfaces ; a flank formed on an outer peripheral surface extending between the top and bottom surfaces; and a cutting edge formed on an intersection portion between the rake face and flank, the cutting edge comprising an arc-shaped cutting edge being curved in an arc shape and located on at least one of nose portions , a working cutting edge extending from one side of the arc-shaped cutting edge , and a linear cutting edge extending from the other side of the arc-shaped cutting edge , wherein a chip breaker groove is formed on the rake face over the periphery of the cutting edge , a chip-breaker concave portion , which is provided between the nose portion and a breaker projection , is formed in the vicinity of the arc-shaped cutting edge on the rake face , the chip breaker groove is formed adjacent to the chip-breaker concave portion and the breaker projection ; the breaker projection projects from a bottom surface portion of the chip-breaker concave portion and a bottom portion of the chip breaker groove ; the chip-breaker concave portion increases the wall surface of the chip breaker in height, as compared with the chip breaker groove ; and the chip-breaker concave portion is defined by an inclined surface which is curved in a concave manner and which is smoothly connected to a bottom surface portion while being gradually inclined toward the bottom surface portion , from a peripheral edge portion on the nose portion side to the bottom surface portion , characterised in that a ridge line of a peripheral edge portion on the working cutting edge side of the chip breaker concave portion is formed so as to extend away from the nose portion as it extends away from the cutting edge . a rake face with a chip breaker which is formed on at least one of top and bottom surfaces ; a flank formed on an outer peripheral surface extending between the top and bottom surfaces; and a cutting edge formed on an intersection portion between the rake face and flank, the cutting edge comprising an arc-shaped cutting edge being curved in an arc shape and located on at least one of nose portions , a working cutting edge extending from one side of the arc-shaped cutting edge , and a linear cutting edge extending from the other side of the arc-shaped cutting edge , wherein a chip breaker groove is formed on the rake face over the periphery of the cutting edge , a chip-breaker concave portion , which is provided between the nose portion and a breaker projection , is formed in the vicinity of the arc-shaped cutting edge on the rake face , the chip breaker groove is formed adjacent to the chip-breaker concave portion and the breaker projection ; the breaker projection projects from a bottom surface portion of the chip-breaker concave portion and a bottom portion of the chip breaker groove ; the chip-breaker concave portion increases the wall surface of the chip breaker in height, as compared with the chip breaker groove ; and the chip-breaker concave portion is defined by an inclined surface which is curved in a concave manner and which is smoothly connected to a bottom surface portion while being gradually inclined toward the bottom surface portion , from a peripheral edge portion on the nose portion side to the bottom surface portion , characterised in that a ridge line of a peripheral edge portion on the working cutting edge side of the chip breaker concave portion is formed so as to extend away from the nose portion as it extends away from the cutting edge . <EOS>