Digital twin has the potential for increasing production, achieving real-time monitor, and realizing predictive maintenance by establishing a real-time high-fidelity mapping between the physical entity and its digital model. However, the high accuracy and instantaneousness requirements of digital twins have hindered their applications in practical engineering. This paper presents a universal framework to fulfill the requirements and to build an accurate and trustworthy digital twin by integrating numerical simulations, sensor data, multi-fidelity surrogate (MFS) models, and visualization techniques. In practical engineering, the number of sensors available to measure quantities of interest is often limited, complementary simulations are necessary to compute these quantities. The simulation results are generally more comprehensive but not as accurate as the sensor data. Therefore, the proposed framework combines the benefits of both simulation results and sensor data by using an MFS model based on moving least squares, named MFS-MLS. The MFS-MLS was developed as an essential part to calibrate the continuous field of the simulation by limited sensor data to obtain accurate results for the digital twin. Then single-fidelity surrogate models are built on the whole domain using the calibrated results of the MFS-MLS as training samples and sensor data as inputs to predict and visualize the quantities of interest in real-time. In addition, the framework was validated by a truss test case, and the results demonstrate that the proposed framework has the potential to be an effective tool to build accurate and trustworthy digital twins.