  We investigate the cosmological consequences of the modified Friedmann
equations when the entropy associated with the apparent horizon, given by
Barrow entropy, $S\sim A^{1+\delta/2}$, where $0\leq\delta\leq1$, represents
the amount of the quantum-gravitational deformation of the horizon. We study
implications of this model in a flat Friedmann-Robertson-Walker (FRW) universe
with/without cosmological constant. Taking the cosmological constant into
account, this model can describe the current accelerated expansion, although
the transition from deceleration phase to the acceleration phase takes place in
the lower redshifts. We investigate the evolution of the scale factor and show
that with increasing $\delta$, the value of the scale factor increases as well.
We also estimate the age of the universe in Barrow cosmology which is smaller
than the age of the universe in standard cosmology.
