We study the localized magnetic states in the semi-Dirac-like system, and find that due to the existence of the saddle point, the magnetic region diminishes greatly with the energy of the saddle point approaching the impurity energy, and reaches a minimum at the energy of the saddle point equal to the impurity energy. A similar feature is observed in the magnetic moment of the impurity. This suppression behavior for the magnetization of the impurity can be understood from the saddle point induced mitigation of asymmetry on the density of state at impurity energy. In contrast, when the saddle point vanishes, due to the opening of the gap, the magnetic region exhibits a monotonous decay when the conduction band edge goes up through the impurity energy. The combined effect of the saddle point and the Coulomb interaction at the impurity on the local magnetization is also investigated.