Presented in this paper is an analytical investigation on column stability of unbraced multi-storey frames with accounting for initial geometric imperfections, namely, out-of-straightness of columns and out-of-plumbness of the frame. Within the context of storey-based buckling and using the end-fixity factor to characterize the beam-to-column rotational restraints, the lateral stiffness of axially loaded columns in unbraced frames with consideration of the effects of the imperfections is derived. The formulations and procedure of calculating storey-based column effective length factors with explicit accounting for the initial geometric imperfections are then proposed. Numerical examples with parametric studies are presented to illustrate the effects of the out-of-straightness and the out-of-plumbness on the column effective length factors and column strengths. The proposed method enables the practitioners to explicitly evaluate column strengths for any given values of the initial geometric imperfections, which is not available in the current design practice.