Abstract-This paper focuses on the development of a cost-aware Bayesian sequential decision-making strategy for the search and classification of multiple unknown objects over a given domain using a sensor with limited sensory capability. Under such scenario, it is risky to allocate all the available sensing resources at a single location of interest, while ignoring other regions in the domain that may contain more critical objects. On the other hand, for the sake of finding and classifying more objects elsewhere, making a decision regarding object existence or its property based on insufficient observations may result in miss-detecting or missclassifying a critical object of interest. Therefore, a decisionmaking strategy that balances the desired decision accuracy and tolerable risks/costs is highly motivated. The strategy developed in this paper seeks to find and classify all unknown objects within the domain with minimum risk under limited resources.