Curvature measurement plays an important role in structural health monitoring, robot-pose measuring, etc. High-resolution curvature measurement is highly demanded. In this paper, an optical curvature sensor with high resolution based on in-fiber Mach-Zehnder interferometer (MZI) and microwave photonic filter (MPF) is proposed and experimentally demonstrated. The in-fiber MZI is constructed with a ring-core fiber (RCF) which is fusion spliced between two coreless fibers (CLFs). The structure of CLF-RCF-CLF is then sandwiched between two segments of single-mode fiber (SMF), making the whole interferometer structure of SMF-CLF-RCF-CLF-SMF. The operating principle is that different curvatures will cause the variations of the interference spectrum of MZI due to elastic-optic effect, and then the variations are converted into the frequency-shift of the MPF. The factors affecting the visibility of the interference spectrum are researched. A preliminary exploration of the multiplexing demodulation for the in-fiber-MZIs is also investigated and discussed, which is for the first time to the best of our knowledge, holding great potential to pave the way for constructing the sensing network composed of interferometric sensors. The curvature measurement sensitivity is -147.634 MHz/m-1, and the resolution is 6.774 × 10-6 m-1 which is the highest value up to now.