The present invention relates to an air compressor and, more particularly, to a compressor that employs the bore of a cylindrical projection, formed at the top wall of a cylinder, as an auxiliary pressure storage chamber. In operation, when the piston reaches the top wall of the cylinder, some compression air can enter the auxiliary pressure storage chamber, which allows the compression stroke of the piston to be performed more smoothly. Furthermore, the cylinder is provided at its one side with an extension wall having a slant bottom edge that substantially covers one half of the entire bottom edge of the cylinder. As such, when the piston reaches the bottom dead center, the piston can be entirely located within the cylinder without escaping therefrom, so that the piston can keep gas-tight with the inner wall of the cylinder during the reciprocating motion of the piston. Accordingly, the air compressor can be operated more securely in addition to an increase of the performance.