For the spreading of an insoluble surfactant-laden droplet over the corrugated topography, the lubrication theory is used to establish the physical and mathematical models of the spreading of droplet and to derive the base state and disturbance evolution equations for thin liquid film thickness and surfactant concentration. The stability of droplet spreading on topography surfaces, as well as the effects of several parameters are investigated based on the non-model stability theory. Results show that disturbance quantities reach minimum at the droplet center and spreading fronts, and achieve the maximum in thinning regions, and the negative disturbance of surfactant concentration is quite obvious. Disturbance wave number can enhance the stability of the droplet spreading, but with increasing wave number, the stability tends to be weak and even transform into instability. The spreading stability is distinctly promoted with decreasing Marangoni number or increasing corrugated topography height. The droplet evolution displays a much stable spreading for moderate values of Peclet number and topography wave number.