The Main-Sequence positions as well as the evolutionary behavior of Population III stars up to an evolution age of 2×1010 yr, taking this time as the age of the Universe, have been investigated in the mass range 0.2 and 0.8M⊙. While Population III stars with masses greater than 0.3M⊙ develop a radiative core during the approach to the Main Sequence, stars with masses smaller than 0.3M⊙ reach the Main Sequence as a wholly convective stars. Population III stars with masses greater than 0.5M⊙ show a brightening of at most 2.2 in bolometric magnitude when the evolution is terminated as compared to the value which corresponds to zero-age Main Sequence. The positions of stars with masses smaller than 0.5M⊙ remain almost the same in the H-R diagram.