The dynamic responses of curved sandwich beams with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and porous core subjected to a low velocity impactor is studied. In order to accurately simulate the dynamic behavior of the sandwich curved beams, a layerwise-finite element approach based on the two-dimensional elasticity theory is employed. The contact force is estimated based on the modified Hertz law. Equivalent mechanical properties of the FG-CNTRC face sheets are determined using a refined rule of mixture approach. After validating the approach, some parametric studies are carried out to examine the influences of carbon nanotube distribution patterns, impactor velocity, the curved beam opening angle, length-to-thickness ratio and core-to-face sheet thickness ratio on the responses of the sandwich curved beams under investigation.