It is challenging to asymptotically stabilize a general two-trailer system consisting of a unicycle car and two identical trailers at a predefined pose efficiently because the system cannot be converted into a chain-form system. In this paper, a two-phase parking strategy is designed for such a system to park at the target pose. The proposed strategy is inspired by a new insight on the singularity set of the general two-trailer system, i.e. the singularity set includes a subset which can be asymptotically stabilized. In the first phase, a tracking controller is adopted to let the state of the system approach the subset. A parking controller is then switched on in the second phase and the system will be asymptotically stabilized at the target pose. Considering its simplicity and efficiency, the proposed controller has a good potential to be used in practice.