Abstract: In this paper, nonlinear Rossby waves for the linear weak shear basic flow are investigated to obtain nonlinear Kubota equation, under certain condition, the Kubota equation reduces to Benjamin-Ono equation. Furthermore, author finds that 1)the larger the amplitude of algebraic solitary Rossby wave and the shear of basic flow, the smaller the propagation speed of algebraic solitary Rossby wave, 2) when the amplitude of algebraic solitary Rossby wave satisfies a certain condition, the phase speed of algebraic solitary Rossby wave decreases with increasing of latitude, and 3) the horizontal structure of algebraic solitary Rossby wave is consistent with dipole blocking in the atmosphere.