We experimentally investigate the passive mode-locking operation of a figure eight-fiber laser based on a symmetrical nonlinear optical loop mirror (NOLM) with a highly twisted low-birefringence fiber in the loop. NOLM switching is achieved by the polarization asymmetry between the counterpropagating beams in the loop. The most efficient switching is obtained when we have linear polarization for one of the beams and the circular polarization for the other. We used a quarter-wave retarder (QWR) in the NOLM loop to break the polarization symmetry. Through the QWR position, it is possible to adjust the transmission behavior from a maximum to a minimum at a low input power. With our configuration, it is possible to get self-starting modelocking operation at a specific position of the QWR. This QWR position corresponds to a value close to the minimal transmission. The pulse repetition frequency was 0.8 MHz. The mode-locked laser ran in a stable operation for hours. We achieved a stable generation of picosecond pulses with milliwatts of an average output power.