With the equivalent mechanical properties of composite materials, analytical formulae of critical load for an all-composite sandwich column with pyramidal truss core are derived. Four failure modes are considered: macro Euler buckling, macro shear buckling, face-sheet wrinkling and face-sheet crushing. Failure mechanism maps are constructed with the four competing failure modes, and the relationship between the failure mechanism maps and material mechanical properties is discussed. Selected experiments validate the analytical predictions, and reasonable agreement is obtained. Macro shear buckling is the main failure mode for the sandwich column specimens, which is attributed to the low stiffness of core. The final failure loads is related to the strength of the nodes between face-sheets and truss core, so the node strength is the key of improving the failure load. Given by numerical simulations, the failure loads and failure modes agree well with analytical predictions.