The Gaussian effective potential of the double sine-Gordon model in n + 1 dim ensions is computed. Within the Gaussian approximation, we prove that the model is trivial for n ≥ 3 and there exists a Coleman phase transition point for n cr=(n+2π(n+1)/2(α1R+α2R/4)(3-n)/2)/(Γ(1/2(3-n))(α1R+α2R/16)).