Numerous linear and nonlinear controller structures are available to stabilize 6-DOF quadrotors, however, those structures are capable of stabilizing the quadrotors in a local region only containing the hovering configuration. This article focuses on the design of a nonlinear controller to achieve the stabilization in large for these unmanned aerial vehicles in hovering configuration at the desired attitude. In this manner, a specific set of state variables is introduced to avoid the singularity problems. Afterwards, a candidate Lyapunov function is considered and the stability is proved based on that function by solving a set of ordinary and partial differential equations, the so-called matching conditions. Then, the asymptotic stability of the desired configuration in 6-DOF is proved using LaSalle's invariant set principle with the region of attraction containing almost all state space. Numerical simulation results are included to validate the feasibility of the proposed almost globally stabilizing controller.