Double-decker filaments and their eruptions have been widely observed in recent years, but their physical formation mechanism is still unclear. Using high spatiotemporal resolution, multi-wavelength observations taken by the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we show the formation of a double-decker pair of flux rope system by two successive tether-cutting eruptions in a bipolar active region. Due to the combined effect of photospheric shearing and convergence motions around the active region’s polarity inversion line (PIL), the arms of two overlapping inverse-S-shaped short filaments reconnected at their intersection, which created a simultaneous upward-moving magnetic flux rope (MFR) and a downward-moving post-flare-loop (PFL) system striding the PIL. Meanwhile, four bright flare ribbons appeared at the footpoints of the newly formed MFR and the PFL. As the MFR rose, two elongated flare ribbons connected by a relatively larger PFL appeared on either side of the PIL. After a few minutes, another MFR formed in the same way at the same location and then erupted in the same direction as the first one. Detailed observational results suggest that the eruption of the first MFR might experienced a short pause before its successful eruption, while the second MFR was a failed eruption. This implies that the two newly formed MFRs might reach a new equilibrium at relatively higher heights for a while, which can be regarded as a transient double-decker flux rope system. The observations can well be explained by the tether-cutting model, and we propose that two successive confined tether-cutting eruptions can naturally produce a double-decker flux rope system, especially when the background coronal magnetic field has a saddle-like distribution of magnetic decay index profile in height.