A special kind of axicon prisms for beam transformation and enhancement of axial trapping force in a single beam gradient optical trap is put forward. By inserting a pair of axicons into the parallel illumination path of a trapping objective, a center weighted TEM 00 Gaussian beam was transformed into an edge weighted beam. Edge weighted illumination for the trapping objective was thus realized, which is significant for the enhancement of axial trapping force. Based on a method of external sinusoidal excitation and lock in detection, we precisely calibrated the axial spring constants of the same optical trap under different illumination conditions. The comparison results confirmed the feasibility of enhancing the axial trapping force by a pair of axicon. Moreover, the strength of enhancement was found to be dependent on the apodization factor for the input TEM 00 Gaussian beam.