A sleeve bore machining apparatus has a plurality of reamers with different diameters, wherein a ball etc. is pressed in and passed through the sleeve bore after a machining with the reamer inserted in the sleeve, measures the push-in load involved in the pass-through operation to select a diameter of the reamer to be used for the next machining process in response to a magnitude of the measured load, or carries out a machining process while a reamer having an edged taper portion or taper stepped portions in a grinding portion is kept inserted in the bore of the sleeve, and controls an extent of insertion of the reamer for the next machining process in response to a magnitude of the measured load, so that the dimensional accuracy of the bore as well as the cylindricity can be successfully machined.