Quantum entanglement serves as an essential resource across various fields, including quantum communication, quantum computing, and quantum precision measurement. Quantum microscope, as one of the significant applications in quantum precision measurement, could bring revolutionary advancements in both signal-to-noise ratio (SNR) and spatial resolution of imaging. Here, we present a quantum microscopy system that relies on a fully fiber-integrated high-performance energy-time entangled light source operating within the near-infrared II (NIR-II) window. Complemented by tailored real-time data acquisition and processing software, we successfully demonstrate the quantum imaging of a standard target, achieving a SNR of 131.51 ± 6.74 and a spatial resolution of 4.75 ± 0.27 µm. Furthermore, we showcase quantum imaging of cancer cells, unveiling the potential of quantum entanglement in biomedical applications. Our fiber-integrated quantum microscope, characterized by high imaging SNR, instantaneous image capture, and analysis capabilities, marks an important step toward the practical application in life sciences.