Flexible sensors with a high sensitivity and wide-frequency response are essential for structural health monitoring (SHM) while they are attached. Here, carbon nanotube (CNT) films doped with various PVA fractions (CNT/PVA) and ZnO nanowires (nano-ZnO) on zinc sheets were first fabricated by functionalized self-assembly and hydrothermal synthesis processes. A CNT/PVA/nano-ZnO flexible composite (CNT/PVA/ZnO) sandwiched with a zinc wafer was then prepared by the spin-coating method. The piezoresistive and/or piezoelectric capabilities of the CNT/PVA/ZnO composite were comprehensively investigated under cyclic bending and impact loading after it was firmly adhered to a substrate (polypropylene sheet or mortar plate). The results show that the piezoresistive sensitivity and linear stability of the CNT/PVA films doped with 20%, 50%, and 100% PVA during bending are 5.47%/mm, 11.082%/mm, and 11.95%/mm and 2.3%, 3.42%, and 4.78%, respectively. The piezoelectric sensitivity, linear stability, and response accuracy of the CNT/PVA/ZnO composite under impulse loading are 4.87 mV/lbf, 3.42%, and 1.496 ms, respectively. These merits support the use of CNT/PVA/ZnO as a piezoresistive and/or piezoelectric compound sensor to monitor the static/dynamic loads on concrete structures while it is attached.