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The trapping stiffness and width are two important parameters to characterize a counter-propagating dual-beam optical trap. We present two types of asymmetric counter-propagating dual-beam optical trap with the different numerical aperture (NA) and trapping power to eliminate the multi-equilibrium positions when two foci of the optical trap are not coincided. Meanwhile, the asymmetric dual-beam trap with the different NA enhances the axial trapping width and stiffness over five and three times, respectively, higher than the standard dual-beam trap with the higher and same average NA. Besides, it increases the transverse trapping stiffness when two foci are not coincided. The asymmetric dual-beam optical trap will benefit the future applications for the study of precision measurement, basic physics and biomaterials. [ABSTRACT FROM AUTHOR]