Three-dimensional wavefront reconstruction of atmospheric turbulence is key technique for star oriented multi- conjugate adaptive optics (SO- MCAO), and the algorithm for three- dimensional wavefront mode reconstruction of atmospheric turbulence in SO-MCAO is analyzed theoretically and researched by simulations. The analysis result shows that the global piston and tip/tilt modes are singular and cannot be localized in altitude due to the fact that piston of turbulence cannot be measured in the case of two turbulence layers by using nature guide stars. Global piston, tip/tilt, defocus, astigmatism modes are singular and cannot be reconstructed in altitude because piston and tip/tilt of turbulence cannot be measured while using laser guide stars. For three turbulence layers, a growing number of singular modals produce enormous aliasing error that cannot be avoided. In spite of the inaccurate wavefront reconstruction for three turbulence layers respectively, the wavefront from observed object can be completely reconstructed if its footprints on layers are fully covered by nature guide stars.