This paper studies the throughput capacity and delay scaling laws in a three-dimensional mobile ad hoc network (3D-MANET) under different routing schemes. Previous work generally assumed that nodes follow a uniform distribution or a power-law distribution to move in the network. From the perspective of the entire network, it is difficult for this network model to reflect communication entities’ distribution in real 3D space. Moreover, the research results of analyzing network performance using different routing schemes are limited, and the research work is insufficient. With formerly related studies different,we propose a cell-gridded network model that considers the actual environment with cells of the node aggregation degree, which follows Zipf’s law with exponent γ . And our model can cover a variety of distribution scenarios with changes in the γ value. The packet delivery rate, network capacity, and delay performance of 3D-MANET adopting the traditional two-hop nonredundant and redundant relay routing scheme are examined utilizing theoretical tools such as probability theory, random process, and queuing theory. We propose a wireless access point- (WAP-) enabled multihop relay routing scheme. By deploying WAP in cells with a high γ , nodes can access WAP and broadcast packets, which accelerates the delivery of packets, and the results obtained by applying this scheme indicate that compared with the two-hop relay scheme, the WAP multihop relay effectively improves the delay performance and the transmission efficiency with less loss of capacity performance. Additionally, a better delay-capacity trade-off performance is achieved. Finally, we discuss the influence of parameters such as the number of network nodes n , the number of network cells m , the redundancy r , and γ on the capacity and delay. The analysis results confirm that exploiting the users’ distribution status information and dividing the cells reasonably will save deployment costs and further improve network performance.