This paper presents the results of the experimental study of a fiber laser connected according to the MOPA scheme, where a power amplifier was made of an ytterbium double-clad tapered spun fiber with low intrinsic birefringence. A peak output power of 160 kW with the average power of 160 W has been achieved at 1040 nm wavelength, 50 ps pulse duration and its repetition frequency of 20 MHz; the laser beam quality parameter and the mode-spot diameter being 1.15 and 35 μm, respectively. The values of azimuth, ellipticity and degree of polarization of the output radiation were found; their little sensitivity to the pump power was demonstrated. This research was the next important step in the development of high-power picosecond fiber lasers technology.