To accelerate a combustion with an entire combustion chamber including the vicinity of an opening portion for air suction to thereby make uniform a flame propagation in a combustion chamber structure for an internal combustion engine, and to provide a technology for preventing the generation of knocks, a longitudinal sectional shape of a top wall surface of the combustion chamber is in the form of a substantially triangular shape in longitudinal section defined and surrounded by a cylinder head, a cylinder and a piston. A projection is provided on a circumferential edge portion of a top surface of the piston, with a surface, facing the top wall surface of the combustion chamber, of the projection being substantially in parallel with the top wall surface of the combustion chamber. A cutaway portion is formed in the vicinity of at least a portion, facing the intake opening portion, of the projection of the top surface of the piston.