In recent times, cloud computing adopted numerous organizations and enterprises for offering services with securely certifying that cloud providers against illegitimate activities. However, cost-effective forensics design and implementation for support the cloud-based cybercrimes investigation. To build cloud architecture support forensics is a significant and complex issue such as voluminous intricate legal, organizational, and technical defies due to the virtualization, distributing, and dynamic nature of cloud systems. Therefore, this paper presents an efficient Cloud Forensics Investigation Model (CFIM) to investigate cloud crimes in a forensically sound and timely fashion. Besides, the proposed system supports the concept of Forensic as a Service (FaaS) that provide innumerable benefits of conducting digital forensics through using Forensic Server on the cloud side. The investigational results proved that the proposed system can assist the digital investigators in their mission of investigation of cybercrimes in the cloud in a proficient manner.