Cloud Computing has emerged as a powerful and promising way for running high performance computing (HPC) jobs. Most HPC jobs are designed under multi-processes paradigm and involve frequent communication and synchronization among parallel processes. However, as the underlying resources of cloud data centers are always shared among multiple tenants, the competition of jobs for limited bandwidth resources lead to unpredictable completion times for jobs in the cloud, which may lead to QoS violation and inefficient utilization of resources when scheduling parallel jobs in the cloud. To tackle the issue, it is essential to provide bandwidth guarantees for parallel jobs running in the cloud. Offering a dedicated virtual cluster (VC) for running applications in the cloud is a popular way to guarantee bandwidth demands. Motivated by these problems, in this paper, we firstly design a time-aware virtual cluster (TVC) request model for parallel jobs and consider how to embed requested TVCs of jobs into cloud efficiently under parallel job scheduling framework. An adaptive bandwidth-aware heuristic algorithm, which is denoted as AdaBa, is proposed to improve the job accept rate by adjusting the priorities of servers to accommodate the VMs of TVC adaptively according to the relative size of requested bandwidth demand. Then, a bandwidth-guaranteed migration and backfilling scheduling algorithm, which is denoted as BgMBF, is designed to schedule parallel jobs and the bandwidth demands are guaranteed by AdaBa. To obtain high job responsiveness performance, a bandwidth-reserved job backfilling strategy is designed when the requested TVC for current scheduled job cannot be allocated in the cloud. The migration cost of BgMBF is also considered and an enhanced version BgMBFSDF is then proposed to minimize the number of migration when the execution time of jobs are known. Through extensive simulation experiments on popular parallel workloads, our proposed TVC embedding algorithm AdaBa achieves up to 15 percent of improvement on accept rate compared with existing algorithms such as Oktupus and greedy algorithm. Our proposed BgMBF and BgMBFSDF also significantly outperform other popular scheduling algorithms integrated with AdaBa on average response time and average bounded slow down.