The non-equilibrium dynamics of spin impurity atoms in a strongly interacting one-dimensional (1D) Bose gas under the gravity field is studied. We show that due to the non-equilibrium preparation of the initial state as well as the interaction between the impurity atoms and other bosons, a counterintuitive phenomenon may emerge: the impurity atoms could propagate upwards automatically in the gravity field . The effects of the strength of interaction, the gradient of the gravity field, as well as the different configurations of the initial state are investigated by studying the time-dependent evolution of the 1D strongly interacting bosonic system using time-evolving block decimation (TEBD) method. A profound connection between this counterintuitive phenomenon and the repulsive bound pair is also revealed. PACS numbers: 03.75.Lm, 05.70.Ln, 05.60.Gg,37.10.JkRecently, ultracold atoms in optical lattice have provided a perfect platform for simulating quantum manybody models in condensed matter physics [1,2]. What's more, the uniqueness of cold atomic system, such as the low dissipation rate as well as long coherence times, has opened exciting possibilities for studying non-equilibrium quantum dynamics of many-body systems. It is known that, due to the energy dissipation between the system and the environment, the properties of the many-body system in solid state physics is mainly determined by its ground state as well as its low-energy excited state. In the ultracold atomic systems, however, the extreme low dissipation rates there guarantees the conservation of the system energy and total particle number in a relatively long time. Therefore, not only the ground state but also the high energy excited state may contribute to the nonequilibrium dynamics of the many-body systems, which may exhibit novel phenomena [3,4,5,6,7,8].Repulsively bound atom pairs is one of the most interesting and novel phenomena emerging from the nonequilibrium many-body physics in optical lattice [9,10]. It is shown that though repulsive force separates particles in free space, under a periodic potential and in the absence of dissipation, a bound atom pairs could be stabilized by the strongly repulsive interaction due to the conservation of energy. This unconventional phenomenon provides a typical example of non-equilibrium physics determined by the high-energy excited state of the Hamiltonian rather than the ground state, and has no analogue in traditional condensed matter systems due to the rapid dissipation. In this Letter, we provide another example of these exotic non-equilibrium phenomena by studying the propagation of spin impurity atoms through a strongly interacting one-dimensional (1D) Bose gas under an external potential which decreases linearly along a particular direction. The ground state and the quench dynamics of the Bose-Hubbard model under linear external potential have been discussed previously [11,12]. We show that if the initial state is prepared far away from the equilibrium ground state, the spin impurity atoms could pro...