In this paper, we study the monotonicity of the ratio of two Abelian integrals \[ I 0 ( h ) = ∫ Γ h y d x and I 1 ( h ) = ∫ Γ h x y d x , I_0(h)=\int _{\Gamma _h}y\,dx\quad \textrm {and}\quad I_1(h)=\int _{\Gamma _h}xy\,dx, \] where Γ h \Gamma _h is a compact component of the level set { ( x , y ) :   y 2 + Ψ ( x ) = h ,   h ∈ J } \{(x,y):\ y^2+\Psi (x)=h, \ h\in J\} ; here J J is an open interval. We first give a new criterion for determining the monotonicity of the ratio of the above two Abelian integrals. Then using this new criterion, we obtain some new Hamiltonian functions H ( x , y ) H(x,y) so that the ratio of the associated two Abelian integrals is monotone. Especially when H ( x , y ) H(x,y) has the form y 2 + P 5 ( x ) y^2+P_5(x) , we obtain the sufficient and necessary conditions that the ratio of two Abelian integrals is monotone, where P 5 ( x ) P_5(x) is a polynomial of x x with degree five.