Large numbers of Urban Air Mobility (UAM) vehicles are expected to operate in urban airspace in the near future, exceeding the capacities of current airspace and Air Traffic Management (ATM) systems. This paper presents an air traffic assignment framework for 3D air transport networks in urban airspace to enable UAM operations at future demand levels. The individual vehicle dynamics are aggregated to describe the overall flow feature in this macroscopic model. Firstly, UAM operations are modeled as flows and structured in a three-dimensional two-way air transport network. Then, a complexity optimal air traffic assignment in urban airspace is formulated as an optimization problem. Based upon the Linear Dynamical System (LDS), a novel complexity metric is defined as objective function, which takes into account dynamic flow structure, congestion, and operational efficiency. A two-phase approach combining Simulated Annealing (SA) and Dafermos’ Algorithm (DA) is introduced to efficiently solve this problem. To validate the proposed model, a case study of an air transport network in Singapore’s urban airspace with two different demands is conducted. Comparative studies are carried out between the proposed algorithm and other widely used traffic assignment algorithms. The results show that the proposed approach is capable of assigning flows in an efficient and effective manner, reducing the complexity of the air transport network significantly. The results also show that optimizing the flow pattern reduces total complexity by 90.44%±0.53% and 92.12%±0.35% with 95% confidence interval, respectively in two scenarios. The framework may be useful for Air Navigation Service Providers (ANSP) in strategic planning for UAM operations and urban airspace design. •A novel macroscopic problem formulation for air traffic assignment in Urban Air Mobility (UAM) operations.•An efficient representation of air transport network for UAM.•An intrinsic air traffic complexity metric based on the Linear Dynamical Systems (LDS).•A two-phase optimization procedure on the basis of Simulated Annealing (SA) and Dafermos’ Algorithm (DA).•Application and comparative study on an air transport network in Singapore’s urban airspace.