Provide is a single-hole double-cutting-edge skew-symmetric pencil-lead-unbroken pencil sharpener. Two blades which are symmetrically installed on the same knife rest are utilized to cut the same pencil with equal force simultaneously and synchronously. The principle is that lever prying force of a single-edge pencil sharpener is changed to be cutting force dipole moment, wherein double sides of the cutting force dipole moment are reversed and are of the same size, and thereby a pencil core is enabled to keep unbroken in the process of cutting. The single-hole double-cutting-edge skew-symmetric pencil-lead-unbroken pencil sharpener comprises the knife rest and the blades. A coarse straight circular pipe section, a conical cavity body cutting groove and a circular fine through hole are communicated in a coaxial-core mode. Grooves, screw spikes, a knife rest base seat and circular cylinder protrusions are arranged on two inclined planes outside the knife rest. The single-hole double-cutting-edge skew-symmetric pencil-lead-unbroken pencil sharpener has the advantages of being small, exquisite and portable like the single-edge pencil sharpener, unbroken in pencil core like a hand-operated pencil sharpener and capable of being installed inside an outer shell of the single-edge pencil sharpener and being beautified by the outer shell. The cutting speed, the efficiency and the service life of the single-hole double-cutting-edge skew-symmetric pencil-lead-unbroken pencil sharpener are all improved by many times. The single-hole double-cutting-edge skew-symmetric pencil-lead-unbroken pencil sharpener only has one more blade than the single-edge pencil sharpener and is simple in structure, easy to manufacture, low in cost and particularly suitable for cutting soft colorful pencil cores, eyebrow pencils used by ladies and the like.