PFS (Prime Focus Spectrograph), a next generation facility instruments on the Subaru telescope, is a wide-field, massively multiplexed, and optical & near-infrared spectrograph. In the PFS cosmology survey, emission line galaxies (ELGs) in the wide redshift range from z= 0.6to2.4 over 1400 square-degree will be observed. The unique redshift range for the PFS cosmology survey is at z>2. We envision that we will start our survey from 2022, and I will describe strategies to achieve the scientific goals as well as the possible systematic problems for future fiber-fed spectroscopic surveys.