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In this paper, we discuss the existence of the positive time periodic mild solutions for the evolution equation in an ordered Banach space E, We apply the operator semigroup theory and the Leray-Schauder fixed point theorem to obtain the existence of a positive ω-periodic mild solution under the condition that the nonlinear function satisfies a linear growth condition concerning the growth exponent of the semigroup T(t) (t ≥ 0). In the end, an example is given to illustrate the applicability ofdoi:10.1186/s13662-015-0435-5 fatcat:kpnqzf52ivhx7al6dlydqudume