Simultaneously increasing the sensitivity and dynamic range of an optical fiber sensor is desired and yet challenging. In this article, we demonstrate an optical fiber curvature sensor based on a no-core fiber (NCF) cascaded with a hollow-core fiber (HCF), realizing simultaneously high sensitivity and a large dynamic range with the assistance of machine learning analysis. The sensor is fabricated by simply fusion splicing a section of NCF and HCF to two single-mode fibers (SMFs), forming the SMF-NCF-HCF-SMF hybrid structure. It is shown that the multimode interference in the NCF can increase the sensitivity of the device for curvature measurements, compared to the conventional SMF-HCF-SMF structure. However, the enhanced sensitivity poses a limitation on the dynamic range of the proposed curvature sensor. We propose the use of machine learning to analyze the measured spectra of the sensor device, achieving one-to-one mapping between the measured raw spectrum and the exerted curvature on the sensor, and thereby the issue of the limited dynamic range is resolved. The proposed strategy, enabling the co-existence of high sensitivity and a large dynamic range, is a highly generalizable technique and can be extended to other optical fiber sensors for measuring other physical, chemical, and biological quantities in different applications.