We study the dynamics of the quantum steering between two separated qubits trapped in a one-dimensional plasmonic waveguide. By numerical methods, we calculate the quantum steerability and other quantum correlations, i.e., entanglement, discord, and coherence, for both cases with and without laser driving fields. It is found that steerability may exhibit a sudden disappearance and sudden reappearance phenomenon. Specifically, there exist time windows with no steerability but finite entanglement. The effects of plasmon wave number and the distance between the two qubits on steerability are also examined. Furthermore, we show that quantum steerability is tunable by adjusting the laser driving fields.