Fiber reinforced polymer(FRP) is one of the most ideal materials for building transmission tower. The elastic and inflective theory about FRP axial compression component is introduced firstly. The equivalent initial bending rate is obtained based on the tested value of ultimate bearing capacity so that the effects of initial bending, residual stress, bushing at the ends and etc are considered. Furthermore, the critical stress and stability coefficient are derived, on which the effects of diameter-thickness ratio and ageing are studied.