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The purpose of this research is to present a matrix method for solving system of linear Fredholm integro-di erential equations(FIDEs) of the second kind on unbounded domain with degenerate kernels in terms of generalized Laguerre polynomials(GLPs). The method is based on the approximation of the truncated generalized Laguerre series. Then the system of (FIDEs) along with initial conditions are transformed into the matrix equations, which cor- responds to a system of linear algebraic equations with the unknown gen- eralized Laguerre coecients. Combining these matrix equations and then solving the system yields the generalized Laguerre coecients of the solution function. In addition, several numerical examples are given to demonstrate the validity, eciency and applicability of the technique