According to the accuracy specifications of telescope goniometry, error sources of sacle tape grating encoder and the angle measuring principle of multi reading head are analyzed. A 4-reading heads angle measurement program which have 90° phase difference, have been developed. And we make counterclockwise and clockwise angle measuring experiments on an azimuth turntable of telescope through harmonic processing and error compensation, and two sets of experiments measuring angle error RMS values of 0.42" and 0.41" are obtained. Experiment results show that the effect of shafting errors, processing error of installation position and partly roundness error for installation torus on the angular measurement accuracy is eliminated by harmonic processing and phase difference method, and high precision angle measurement with sub-arc-second-accuary is achieved. The research results are useful for analyzing and distributing errors, forecasting angle measuring accuracy and reducing design and machining errors in the design of large aperture telescopes.