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For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of Green function. The asymptotic behavior, as ε → 0 , of G ε (x , t ; y , s) and ∇ x G ε (x , t ; y , s) as well as ∇ x ∇ y G ε (x , t ; y , s) are obtained. These results will be used to investigate the boundary layer phenomena and higher-order convergence in periodic homogenization. To the author's best knowledge, our results are new even for the time-independent case. [ABSTRACT FROM AUTHOR]