This paper investigates the existence of solutions for a class of variable exponent integrodifferential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies sub-$(p^{-}-1)$ growth condition or general growth condition, we give the existence of solutions and nonnegative solutions via Leray-Schauder degree at nonresonance, respectively. Moreover, the existence of solutions for the problem at resonance has been discussed.