Three-dimensional mobile ad hoc networks (3D MANETs) are a class of flexible and distributed peer-to-peer networks, where mobile nodes move within 3D space and can communicate with each other via wireless link without any pre-existing infrastructure. As 3D MANETs can be rapidly deployed and flexibly reconfigured, they are appealing many critical applications: various military units communication (i.e., aircrafts, troops, and fleets) for modern combat, underwater vehicles communication for ocean surveillance, and unmanned aerial vehicles communication for disaster monitoring. To support these applications with different delay requirements in 3D MANETs, understanding the packet delivery delay performance in such networks is of fundamental importance. The packet delivery delay performance for 2D MANETs has been extensively studied in the literature, in terms of its order sense scaling laws with network size or its closedform analytical models (see Section II for related work). However, all the above work is conducted on 2D MANETs only. Recently, some initial work has focused on the study of performance for 3D MANETs, such as throughput capacity [1] and delivery rate [2], which are defined as the maximum packet input rate that the network can stably support and the probability that a packet is successfully transmitted to its destination, respectively. It is notable that the packet delivery delay performance in 3D MANETs has not been investigated, which significantly hinders their applications. Different from the aforementioned work, this paper studies the packet delivery delay performance in 3D MANETs. This paper made a significant improvement on our previous work of [3]. In [3], we only studied the packet delivery delay. In this paper, we study the packet delivery delay as well as corresponding relative standard deviation.