The alignment errors of primary and secondary mirrors can make the image blur. In order to improve the alignment precision of the telescope′s primary and secondary mirrors, an algorithm used to calculate the alignment errors based on astigmatic decomposition is presented. The algorithm makes use of the astigmatism itern of wavefront errors described by Zernike Polynomials to calculate the astigmatism produced by the different alignment errors independently. The character of the astigmatic decomposition algorithm is investigated based on a reflective coaxial (RC) telescope whose diameter is 1200 mm. It is obviously that the calculation errors increase along with the distance between the primary and secondary mirrors′ optical axes, while the two optical axes are in the different planes. An alignment algorithm is designed based on the astigmatic decomposition algorithm. The simulation alignment is done. The simulation shows that the alignment algorithm can align the optical system rapidly with a residual less than 5 μm and 0.5″, when the distance between two axes is less than 0.5 mm and the tilt of two axes is less than 0.1°. Simulation analysis demonstrates the feasibility of the alignment algorithm based on astigmatic decomposition.