This paper focuses on the control design problem of a tethered drone. The suggested concept has the potential to solve some basic difficulties related to the use of small drones, such as their short flight duration, limited lifting ability and the need of precise indoor position sensing. Here, the end of the tether is connected to the drone, while the other side is wrapped on a spool driven by a DC motor, fixed on the ground. Under the assumption that the tether is kept taut at all time, a full autonomous flight can be achieved indoors, where the tether functions as a position sensor. The tether is pulled from its two sides, by the ground motor and the drone. Critical constraints, driven from this configuration, demand positive tether tension and limited flight space. Hence, a unified model is developed for the combined ground-aerial system, and a model predictive control approach is taken, to allow for optimal control under state and input constraints. Simulations results show the performance of the design for both set-point and trajectory tracking cases.