Structure of premixed laminar edge-flame in counterflow field with a strain rate gradient was investigated by numerical simulation. Two-dimensional incompressible Navier-Stokes equations with full chemistry of CH₄/air were solved in curvilinear coordinates. When the strain rate gradient was produced by inclining an axis of the burner, the edge-flame was observed at the side of higher strain rate. On the other hand, the structure of twin flames in the side of lower strain rate was similar to that of normal counterflow premixed flame with no strain rate gradient, and therefore temperature and mole fractions of species were almost constant along the flame surface. The local strain rates at the edge were constant for an equivalence ratio as same as the extinction strain rates for the normal counterflow flames were.