In the present paper, we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving large and sparse general coupled matrix equations ∑ j = 1 p A i j X j B i j = C i , i = 1 , … , p , where A i j ∈ R m × m , B i j ∈ R n × n , C i ∈ R m × n , i , j = 1 , 2 , … , p , are given matrices and X i ∈ R m × n , i = 1 , 2 , … , p , are the unknown matrices. To do so, first, a new inner product and its corresponding matrix norm are defined. Then, using a linear operator equation and new matrix product, we demonstrate how to employ Gl-FOM and Gl-GMRES algorithms for solving general coupled matrix equations. Finally, some numerical experiments are given to illustrate the validity and applicability of the results obtained in this work.