Regarding the strong magnetic field of neutron stars and high energy regime scenario which is based on high curvature region near the compact objects, one is motivated to study magnetic neutron stars in an energy dependent spacetime. In this paper, we show that such strong magnetic field and energy dependency of spacetime have considerable effects on the properties of neutron stars. We examine the variations of maximum mass and related radius, Schwarzschild radius, average density, gravitational redshift, Kretschmann scalar and Buchdahl theorem due to magnetic field and also energy dependency of metric. First, it will be shown that the maximum mass and radius of neutron stars are increasing function of magnetic field while average density, redshift, the strength of gravity and Kretschmann scalar are decreasing functions of it. These results are due to a repulsive-like force behavior for the magnetic field. Next, the effects of the gravitys rainbow will be studied and it will be shown that by increasing the rainbow function, the neutron stars could enjoy an expansion in their structures. Then, we obtain a new relation for the upper mass limit of a static spherical neutron star with uniform density in gravitys rainbow (Buchdahl limit) in which such upper limit is modified as $M_{eff}<frac{4c^{2}R}{9G}$. In addition, stability and energy conditions for the equation of state of neutron star matter are also investigated and a comparison with empirical results is done. It is notable that the numerical study in this paper is conducted by using the lowest order constrained variational (LOCV) approach in the presence of magnetic field employing AV18 potential.
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