This paper considers the attitude control problem for an all-electric spacecraft during its transfer to the Geostationary Earth orbit. During the transfer, the spacecraft's solar arrays need to point towards the Sun, except in eclipses, in order to operate the onboard electric thrusters. We propose a neural-network based adaptive controller, utilizing a Modified State Observer (MSO) methodology, for the attitude control of the all-electric spacecraft. The MSO generates adaptations to aid a traditional PD controller in tracking the commanded attitude and angular velocity, while the adaptive controller use the state estimation error (instead of the tracking error) to account for the uncertainties. Numerical simulations illustrate the performance of the proposed controller for cases of changing spacecraft moment of inertia due to fuel burn, the presence of a disturbing torque due to thruster misalignment and lack of attitude tracking during eclipses.