Abstract In this paper, we consider a kind of singular integrals which appear in the generalized 2D dissipative quasi-geostrophic (QG) equation ∂ t θ + u ⋅ ∇ θ + κ Λ 2 β θ = 0 , ( x , t ) ∈ ℝ 2 × ℝ + , κ > 0 , \partial_{t}\theta+u\cdot\nabla\theta+\kappa\Lambda^{2\beta}\theta=0,\quad(x,t% )\in\mathbb{R}^{2}\times\mathbb{R}^{+},\;\kappa>0, where u = - ∇ ⊥ Λ - 2 + 2 α θ {u=-\nabla^{\bot}\Lambda^{-2+2\alpha}\theta} , α ∈ [ 0 , 1 2 ] {\alpha\in[0,\frac{1}{2}]} and β ∈ ( 0 , 1 ] {\beta\in(0,1]} . First, we give a relationship between this kind of singular integrals and Calderón–Zygmund singular integral operators and obtain a uniform Besov estimates. As an application, we give the well-posedness of the generalized 2D dissipative quasi-geostrophic (QG) in the critical Besov space.