In this work, InGaN/GaN multiple-quantum-wells light-emitting diodes with and without graphene transparent conductive electrodes are studied with current-voltage, electroluminescence, and time-resolved electroluminescence (TREL) measurements. The results demonstrate that the applications of graphene electrodes on LED devices will spread injection carriers more uniformly into the active region and therefore result in a larger current density, broader luminescence area, and stronger EL intensity. In addition, the TREL data will be further analyzed by employing a 2-N theoretical model of carrier transport, capture, and escape processes. The combined experimental and theoretical results clearly indicate that those LEDs with graphene transparent conductive electrodes at p-junctions will have a shorter hole transport time along the lateral direction and thus a more efficient current spreading and a larger luminescence area. In addition, a shorter hole transport time will also expedite hole capture processes and result in a shorter capture time and better light emitting efficiency. Furthermore, as more carrier injected into the active regions of LEDs, thanks to graphene transparent conductive electrodes, excessive carriers need more time to proceed carrier recombination processes in QWs and result in a longer carrier recombination time. In short, the LED samples, with the help of graphene electrodes, are shown to have a better carrier transport efficiency, better carrier capture efficiency, and more electron-hole recombination. These research results provide important information for the carrier transport, carrier capture, and recombination processes in InGaN/GaN MQW LEDs with graphene transparent conductive electrodes.