The advancement of quantum computing technology has led to the emergence of early-stage quantum cloud computing services. To fully realize the potential of quantum cloud computing, it is essential to develop techniques that ensure the privacy of both data and functions. Quantum computations often leverage superposition to evaluate a function on all possible inputs simultaneously, making function privacy a critical requirement. In 2009, Broadbent et al. introduced the Universal Blind Quantum Computation (UBQC) protocol, which is based on Measurement-Based Quantum Computation (MBQC) and provides a framework for ensuring both function and data privacy in quantum computing. Although theoretical results indicate an equivalence between MBQC and circuitbased quantum computation, translating MBQC into circuitbased implementations remains challenging due to higher qubit requirements and the complexity of the transformation process. Consequently, current quantum cloud computing platforms are limited in their ability to simulate MBQC efficiently. This paper presents an efficient method to simulate MBQC on circuit-based quantum computing platforms. We validate this approach by implementing the two-qubit Grover algorithm in the MBQC framework and further demonstrate blindness by applying the UBQC protocol. This work verifies the simulation of a blind quantum computation using the two-qubit Grover algorithm on a circuit-based quantum computing platform.