In this work, we have fabricated the conventional organic light-emitting diodes which are based on the promising rubrene material and their magneto-conductances (MCs) of the device have been measured at various temperatures and injection currents. The experimental results demonstrate that the current- and temperature-dependent MC curves of the device mainly show three structures as the magnetic field increases. Specifically, at room temperature (300 K), under low magnetic field (| B | 1 shows a rapid enhancement with increasing magnetic field at low currents, slowly rises and then decreases at moderate currents, and slowly decreases at high currents; in the medium magnetic field range (6 mT B |<17 mT), as magnetic field increases, MC 2 shows a slow rise in each current range; in the high magnetic field range (17 mT B | 3 rapidly reduces with increasing applied magnetic field in each current range. In order to further research the temperature effect on the MC responses, we also take the current of 50 μA as an example and measure the MC curves at different temperatures. Surprisingly, we found that temperature dependences of MC curves possess similar line-shape with current-dependent MC curves at ambient temperature. That is, with decreasing temperatures, in the low magnetic field range (| B | 1 demonstrates a slow rise at 300 K, slowly rises and then decreases at 250 and 150 K, and then slows down gradually at 100 and 20 K; in the medium magnetic field range (6 mT B | 2 shows a slow rise in each temperature range; in the high magnetic field range (17 mT B | 3 rapidly reduces with increasing applied magnetic field in each temperature range. On the whole, the line-shapes of MC 2 and MC 3 curves remain almost unchanged with decreasing temperatures (or increasing injection currents) in the medium and high magnetic field ranges (| B |>6 mT), but the tendency of MC 1 curves corresponding to low magnetic field (| B |<6 mT) will change with injection currents and temperatures. Additionally, by further analyzing the double logarithmic and temperature-dependent current density-voltage curves, we find that some traps which were usually originated from the fabrication process of devices inevitably exist in the device at room temperature and small injection currents, and the number of traps increases with decreasing temperature. Therefore, in addition to the dissociation of the triplet excitons by free charges (T+Q ® e+h+Q) and the intersystem crossing between singlet and triplet polaron pairs (PP 1 ® PP 3 ), two kinds of trap-assisted triplet exciton quenching processes (that is, trapped triplet-free polaron interaction (T t +P ® S 0 +P t ) and free triplet-trapped polaron interaction (T+P t ® S 0 +P)) are also included in the device. The combined effects of these four microscopic mechanisms lead to a complicated structure of the MC curves at small field and could be well tuned by device current density and working temperature. But the line-shapes of high-field MC responses are mainly determined by the role of TQA process. This article not only deepens the mechanism understanding of triplet-charge interactions in rubrene devices, but also enriches the manifestations of organic magneto-conductance curves.