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In this paper, the effect of slenderness ratio on the ultimate stability bearing capacity of the eccentric compressive members is analyzed. 10 specimens are analyzed by ABAQUS finite element software and steel structure code at home and abroad. This case is that the eccentric load is applied at both ends. The eccentric distance is 27.1mm. The slenderness ratios are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100, respectively. The results show that the numerical simulation results considering the initial imperfection are in good agreement with the theoretical results, and the two rules is similar; the results of standard calculation are basically the same in all countries; with the increase of slenderness ratio, the ultimate load decreases; as the slenderness ratio increases, the slope of the softening stage increases, which inflects a shift from ductility to instability; however, when the slenderness ratio is equal to or greater than 50, the transition of instability to ductility is expressed, and we can define this value as the critical value of different failure patterns.