Infrastructure as a Service (IaaS) generally provides a standard vanilla server that contains an OS and basic functions, and each user has to manually install the required applications for the proper server deployments. We are working on a composite application deployment approach to automatically install selected applications in a flexible manner, based on a set of application installation scripts that are invoked on the vanilla server. Some applications have installation dependencies involving multiple servers. Previous research projects on installing applications with multi-server dependencies have deployed the servers sequentially. This means the total deployment time grows linearly with the number of servers. Our automated parallel approach makes the composite application deployment run in parallel when there are installation dependencies across multiple servers. We implemented a prototype system on Chef, a widely used automatic server installation framework, and evaluated the performance of our composite application deployment on a SoftLayer public cloud using two composite application server cases. The deployment times were reduced by roughly 40% in our trials.