A fiber-optic probe consisting of a section of graded-index multimode fiber (GIMF) fused onto a few-mode fiber (FMF) is proposed in this paper. The orbital angular momentum (OAM) mode guided by the FMF was launched into the GIMF, and a focused OAM beam profile was obtained by tailoring the length of the GIMF. Based on the analysis of the propagation trajectory, the intensity distributions, and the phase distributions of the vortex beam in GIMF, the focusing properties of the OAM mode were investigated. It is found that there exists a maximum working distance at an optimal GIMF length, and a trade-off between the beam size and working distance should be taken into account for optical tweezer applications. These results are expected to be applied to optical fiber tweezers for more flexible and efficient optical manipulation of particles.