In　the　numerical　prediction　of　the　homogenized　macroscopic　properties　of　arbitrary　heterogeneous　material　with　periodic　microstructure,　a　general　formulation　of　the　first-order　perturbation　based　stochastic　homogenization(FPSH)　method　was　presented　in　a　discretized　form　by　finite　element　method　in　order　to　consider　multiple　random　parameters　of　the　mechanical　properties　in　the　constitutive　models.　Many　random　parameters　were　defined　for　each　material　model　and　for　each　component　of　the　stress-strain　matrix　of　the　constituent＇s　material　model.　In　order　to　demonstrative　the　effectiveness　of　above　formulation,　the　numerical　predictions　of　3D　printed　cellular　structure　is　implemented.　Firstly,　the　variation　in　the　mechanical　properties　is　quantified　in　3D　printed　cellular　structure　by　considering　statistical　nature　of　the　defects.　After　manufacturing,　the　Computed　Tomography　(CT)　technology　was　used　to　observe　the　microstructure　in　order　to　evaluate　the　performance　of　printed　structure.　In　the　raw　material,　the　defects　were　characterized　and　categorized　into　three　main　groups,　i.e.　notch,　kink　and　hole.　The　mechanical　properties　differ　portion　by　portion　due　to　above　defects.　Therefore,　the　FPSH　method　was　utilized　to　predict　the　expected　and　variance　of　homogenized　elastic　properties.　This　study　can　contribute　to　improve　the　manufacturing　accuracy　in　other　3D　printed　structure　by　employing　the　statistical　data　of　defects.　Moreover,　the　micro　stress　was　discussed　at　the　end　to　get　a　better　solution　of　both　macroscopic　stiffness　and　strength　of　cellular　structure.