High precision pointing and tracking is an important performance indicator of the telescope, and tracking is implemented mainly by the azimuth axis and the altitude axis movement together method for alt-azimuth designed telescopes, and as a control feedback angle encoder must be installed on the azimuth axis, pitch axis. Scale tape grating encoder due to the advantages of non-contact measurement, high precision, simple assembly and adjustment, as a new generation of angle encoders has been widely used in modern telescopes’ angle measuring system. However performance of these systems can be limited by the factors of mechanical installation, machining error, random error, and other types of error, which often fail to meet arcsecond or sub-arcsecond angle measurement requirements. This paper analyzes the impacts of the mechanical installation eccentric, the roundness error, shafting sloshing on encoder angle measuring, and develops a 4 reading heads, which have 90 ° phase difference, software subdivision angle measurement program. And we make counterclockwise and clockwise angle measuring experiments on a experimental platform, which has mechanical installation eccentric 10um, roundness error 2um and shafting sloshing 0.6". Two sets of experiments measuring angle error RMS values are 0.387'' and 0.487''. The experiments prove that the program can eliminate the angular measurement error due to the mechanical installation the eccentric, machining roundness error, shafting sloshing, achieve arcsecond angle measuring.