The self-focusing/defocusing of Hermite-sinh-Gaussian (HshG) laser beam in underdense inhomogeneous plasmas is studied by using higher-order approximation theory. It is found that Hermite mode index and the fluctuation of the periodic plasma density have a significant effect on the dielectric constant and laser beam self-focusing/self-defocusing. With the increase of mode index, the high-order HshG laser beam is beneficial to suppress self-focusing and enhance self-defocusing. In addition, the effects of decentered parameters, beam intensity, and plasma non-uniformity on self-focusing/self-defocusing are discussed.