A detailed theoretical study on the mode correlation and coherent-mode representation of multi-mode laser beams has been performed.By using the theory of partially coherent light,the multi-mode laser beams behaving like Gaussian Schell-model(GSM) beams have been represented by the superposition of spatially coherent modes,which may be mutually correlated.The analytical expressions for the mode coherence cofficients have been given in the rectangular coordinate system.Furthermore,based on the M2-factor concept,the theory of the mode decomposition of multi-mode laser beams has been built up for the general case,where the mode correlation is considered.