This paper introduces the short packet transmission in non‐orthogonal multiple access (NOMA)‐based unmanned aerial vehicle (UAV) assisted relay communication system. Short packet transmission has considerable potential to decrease the transmission latency of UAV communication, and NOMA can effectively enhance the spectrum efficiency and fairness. To improve the reliability of the system, an effective packet error rate (PER) minimization problem within short packet transmission is proposed by jointly optimizing the packet length, UAV placement, and power allocation under the reliability requirement and total power constraints. To address the intricate PER minimization problem, the optimization problem is firstly decomposed into three sub‐problems, and the corresponding monotonicity and convexity are analyzed, respectively. Then, an overall iterative optimization algorithm for PER minimization based on alternating direction method of multipliers algorithm and optimal solution algorithm is formulated by solving the three sub‐problems in an iterative manner. Simulation results validate the effectiveness and convergence of the proposed NOMA scheme and overall iterative optimization algorithm, respectively.