In this paper, we investigate the transmission delay of cache-aided broadcast networks with user cooperation. Novel coded caching schemes are proposed for both centralized and decentralized caching settings, by efficiently exploiting time and cache resources and creating parallel data delivery at the server and users. We derive a lower bound on the transmission delay and show that the proposed centralized coded caching scheme is \emph{order-optimal} in the sense that it achieves a constant multiplicative gap within the lower bound. Our decentralized coded caching scheme is also order-optimal when each user's cache size is larger than the threshold $N(1-\sqrt[{K-1}]{ {1}/{(K+1)}})$ (approaching 0 as $K\to \infty$), where $K$ is the total number of users and $N$ is the size of file library. Moreover, for both the centralized and decentralized caching settings, our schemes obtain an additional \emph{cooperation gain} offered by user cooperation and an additional \emph{parallel gain} offered by the parallel transmission among the server and users. It is shown that in order to reduce the transmission delay, the number of users parallelly sending signals should be appropriately chosen according to user's cache size, and alway letting more users parallelly send information could cause high transmission delay.