  In this work, we have first obtained the hydrostatic equilibrium equation in
dilaton gravity. Then we have examined some of the structural characteristics
of strange quark star in dilaton gravity with a background of Einstein gravity.
We have shown that the variations of dilaton parameter do not affect the
maximum mass of quark star, while the variations of the cosmological constant
lead to change in the structural characteristics of the quark star. We have
investigated the stability of strange quark stars that studied by MIT Bag
model, in dilaton gravity. We have also provided limiting values for the
dilaton field parameter and the cosmological constant.We have also studied the
effects of dilaton gravity on the other properties of quark star such as the
mean density and gravitational redshift. We have concluded that the last
reported value for cosmological constant does not affect on maximum mass of
strange quark star.
