We propose and demonstrate a novel single fiber optical tweezer based on a graded-index multimode fiber (GIMMF), which works with a free length GIMMF (>30cm). We achieve a three-dimensional stable trap of yeast cells by using the GIMMF optical tweezers. Compared with the single-mode fiber optical tweezers, the GIMMF optical tweezers possess large optical trapping forces. Owing to the freedom of the GIMMF length, the fabrication of the GIMMF optical tweezers is simple, repeatable, and highly efficient. The GIMMF tweezers have the penitential to become a new member of the single fiber optical tweezers family and have a wide range of applications in the medical and biological cytology fields.