Scientific workflow execution in edge-cloud platform have attained in-creased attention, due to reduction in overall makespan assuring workflow deadlines. The workflow task is composed of diverse subtasks which are either executed in edge and the cloud; they are prone to security risk. Any loss of security breach will result to privacy and data integrity issues. Thus, providing security and meeting workflow execution strict deadlines becomes extremely difficult. The current workflow scheduling methods failed to assure both privacy and integrity together under edge-cloud computing platform. In addressing the research security and efficiency issues, this article introduced a novel approach namely Privacy-Integrity Aware Efficient Workflow Scheduler (PIAEWS) for edge-cloud platform. The PIAEWS introduces a novel trust metrics to assure only authenticated node takes part communication and consensus model to assure data integrity without compromising on user privacy constraint. The PIAEWS improves makespan and reduces overall energy consumption by assuring both security and performance together when executing genome sequencing workflow application in edge-cloud platform.