Three-axis attitude control using only magnetic actuators has been considered a difficult task due to earth's time-varying magnetic field, the inherent under-actuation associated with this task, and constraints on control dipole moments. In this study, a linear time-varying model predictive control approach is applied to magnetically actuated satellites in elliptic low-earth orbits for nadir and inertial pointing. A linear time-varying model predictive control problem is formulated using an augmented state-space model based on small-angle approximations for both nadir and inertial-pointing nonlinear dynamics models. To reduce the on-line computational load, the model predictive control design for an inertial-pointing problem with Laguerre functions is proposed, and exponential data weighting is used to improve the numerically ill-conditioned problem. Nonlinear simulation results demonstrate the effectiveness of the proposed method.