The invention relates to the field of single-screw compressors, in particular to a single-screw compressor with the design of the maximum angle of engagement (at) of a screw and a star wheel meshing pair. A cylindrical screw and two plane star wheels with symmetrically arranged centers form a meshing pair which is installed in a machine shell. A screw spiral trough, the inner wall of the machine shell and the top surface of a star wheel disc tooth form a closed element cubage. Along with rotation of screw star wheel teeth, the closed element cubage is changed, air enters an intake cavity and a screw tooth socket space from a screw chamfer end face, a rotated star wheel tooth disc is compressed to achieve the design pressure after being closed, and air is discharged through an exhaust channel from an exhaust triangular notch arranged on the inner wall of the machine shell. The maximum angle of engagement (at) of the screw and the star wheel meshing pair is no more than 98 degrees and no less than 94.5 degrees. The invention has the advantages that the delivery capacity of the single-screw compressor and the cube of the diameter d1 of the screw are in direct ratio with the maximum influence. By adopting the design of a large angle of engagement (at), for the single-screw compressor with the same delivery capacity, when the diameter d1 of the screw is minimum, the volumetric efficiency is maximum.