To provide a cutting insert, a cutting tool, an automatic lathe and a center hole processing method, high in a processing grade by generating a stable grinding line.

A work 19 is vertically installed on a rotary base 57 of the automatic lathe 53. A holder 9 attached with the cutting insert 1 is horizontally installed on a tool post 59 on the side of the work 19. The work 19 is rotated in the arrow A direction, and the holder 9, thus, the cutting insert 1 is lowered obliquely downward (the left lower side of the figure : at an angle of 45° from the horizontal). That is, the cutting insert 1 is obliquely lowered (in the arrow B direction) toward a depth position Y from a processing end surface 61 in a rotary shaft 63 from a side position X separated to the right side from the rotary shaft 63 in the processing end surface 61 of the work 19 so as to form a conical center hole 17.