The International Telecommunication Union has required that the control plane (C-plane) latency in the fifth generation (5G) ultra-reliable low-latency communication (URLLC) application scenarios should not exceed 20 ms and encouraged technical innovation to further reduce it to less than 10 ms. However, the average C-plane latency in the fourth generation (4G) Long Term Evolution-Advanced (LTE-A) system is 80 ms. Such a high latency is because of the execution of the contention-based random access procedure (RAP). In this paper, we simplify the conventional contention-based RAP from 4 to 2 steps. Furthermore, utilization of demodulation reference signal for representing the UE ID and reservation of preambles for URLLC users significantly reduces the proposed 2-step RAP latency. From the perspectives of fixing the number of URLLC users and fixing the number of preambles reserved for URLLC users, simulation results show the percentage of successes for the 2-step RAP is 83.81% and 71.83% higher than that of the 4-step RAP, respectively. Consequently, the 10 ms latency requirement of the 5G URLLC is achieved.