  As is pointed out in a recent work (Phys. Rev. Lett. 120, 222001), quark
matter may not be strange. Inspired by this argument, we use a new
self-consistent mean field approximation method to study the equation of state
of cold dense matter within the framework of the two-flavor NJL model. Then the
mass-radius relationship of two-flavor pure quark stars is studied. In the new
self-consistent mean field approximation method we introduced, there is a free
parameter $\alpha$, which reflects the weight of different interaction
channels. In principal, $\alpha$ should be determined by experiments rather
than the self-consistent mean field approximation itself. In this paper, thus,
the influence of the variation of $\alpha$ on the critical chemical potential
of chiral phase transition and the stiffness of the EOS are thoroughly
explored. It is found that the stiffness of EOS can be increased greatly to
support a two-solar-mass pure quark star when $\alpha$ is greater than 0.95.
This means that current theoretical calculations and astronomical observations
cannot rule out the possibility of a two-flavor pure quark star.
