Stem cell competition could shed light on the tissue-based quality control mechanism that prevents carcinogenesis. To quantitatively evaluate stem cell competition in vitro, we developed a two-color intestinal organoid forming system. First, we improved a protocol of culturing organoids from intestinal leucine-rich-repeat containing G-protein-coupled receptor 5 (Lgr5)- enhanced green fluorescent protein (EGFP)high stem cells directly sorted on Matrigel without embedding. The organoid-forming potential (OFP) was 25{\%} of Lgr5-EGFPhigh cells sorted at one cell per well. Using this culture protocol with lineage tracing, we established a two-color organoid culture system by mixing stem cells expressing different fluorescent colors. To analyze stem cell competition, two-color organoids were formed by mixing X-ray-irradiated and non-irradiated intestinal stem cells. In the two-color organoids, irradiated stem cells exhibited a growth disadvantage, although the OFP of irradiated cells alone did not decrease significantly from that of non-irradiated cells. These results suggest that stem cell competition can be evaluated quantitively in vitro using our new system.