  In this paper, we consider a spherical symmetric metric to extract the
hydrostatic equilibrium equation of stars in $(3+1)-$dimensional gravity's
rainbow in the presence of cosmological constant. Then, we generalize the
hydrostatic equilibrium equation to $d$-dimensions and obtain the hydrostatic
equilibrium equation for this gravity. Also, we obtain the maximum mass of
neutron star using the modern equations of state of neutron star matter derived
from the microscopic calculations. It is notable that, in this paper, we
consider the effects of rainbow functions on the diagrams related to the
mass-central mass density ($M$-$\rho _{c}$) relation and also the mass-radius
($M$-$R$) relation of neutron star. We also study the effects of rainbow
functions on the other properties of neutron star such as the Schwarzschild
radius, average density, strength of gravity and gravitational redshift. Then,
we apply the cosmological constant to this theory to obtain the diagrams of
$M$-$\rho _{c}$ (or $M$-$R$) and other properties of these stars. Next, we
investigate the dynamical stability condition for these stars in gravity's
rainbow and show that these stars have dynamical stability. We also obtain a
relation between mass of neutron stars and Planck mass. In addition, we compare
obtained results of this theory with the observational data.
