In this paper, the L 2 boundedness of the Hilbert transform along variable flat curve (t , P (x 1) γ (t)) H P , γ f (x 1 , x 2) : = p. v. ∫ - ∞ ∞ f (x 1 - t , x 2 - P (x 1) γ (t)) d t t , ∀ (x 1 , x 2) ∈ R 2 , is studied, where P is a real polynomial on R . A new sufficient condition on the curve γ is introduced.