  We present a new class of solutions to the Einstein field equations for an
anisotropic matter distribution in which the interior space-time obeys the
Karmarkar condition. The necessary and sufficient condition required for a
spherically symmetric space-time to be of class one reduces the gravitational
behavior of the model to a single metric function. By assuming a physically
viable form for the $g_{rr}$ metric potential we obtain an exact solution of
the Einstein field equations which is free from any singularities and satisfies
all the physical criteria. We utilize this solution to predict the masses and
radii of well-known compact objects such as Cen X-3, PSR J0348+0432,
PSRB0943+10 and XTE J1739-285.
  To be publish in Chinese Physics C (Accepted)
