The performance in the practical combustion system including reciprocating engines and gas turbine combustors is being much governed by turbulent reacting flow that is often analyzed by both a laminar flamelets concept and flame interaction. The characteristics of laminar flame interaction have been investigated numerically to provide basic understanding of wrinkled turbulent flames under concentration interaction resulting from inhomogeneity in fuel-air mixing, especially focused on the transition of flame characteristics such as diffusion flame, partially premixed diffusion flame, and triple-layer flame by the variation in the degree of premixedness. The extinction stretch rates to the premixedness have also been obtained in this paper. The boundary defining the regime of the existence of triple-layer flames as functions of both stretch rate and premixedness has been determined which agrees well with previously reported experiment measuring OH radical concentration peaks based on PLIF.