Even though current LTE/LTE-A mobile networks provide enough high data rate and low latency to support conventional wireless services, to support ultra-low delay services, such as virtual reality and remote control, in the next generation mobile communication network, it is required to provide very low delay about several ms. However, in the uplink transmission of the LTE/LTE-A system, the process of scheduling grant is required to obtain uplink resources for uplink transmission from the eNB. The process of granting uplink resources from eNB brings additional fixed latency, which is one of the critical obstacles to achieve low delay in uplink transmissions. Thus, in this paper, we propose a novel uplink transmission scheme called Cut-in uplink transmission, to reduce uplink latency. We provide the performance of the proposed uplink transmission scheme through simulations and show the proposed uplink transmission scheme provides lower uplink transmission delay than conventional uplink transmission scheme in LTE/LTE-A mobile networks.