Known as "shape sensing", real-time reconstruction of a structure's three-dimensional displacements using a network of in situ strain sensors and measured strains is a vital technology for structural health monitoring (SHM). The inverse finite element method (iFEM) is a mechanics-based shape-sensing algorithm shown to be fast, accurate, and robust for usage as a part of SHM systems. In this study, a new eight-node curved inverse-shell element, named as iCS8, is developed based on iFEM methodology. The kinematic relations of iCS8 element are established through combining kinematics of solid shell together with kinematic assumptions of first-order shear deformation plate theory. The new weighted-least-squares functional of iFEM uses the complete set of section strains consistent with the iCS8 element, i.e., (1) coupled membrane-bending and (2) transverse-shear section strains. The iCS8 element accommodates a curvilinear isoparamettic coordinate system, thus it can be effectively utilized to model cylindrical/curved geometries with a coarse discretization. This practical modelling capability can allow a relatively sparse placement of sensors, therefore providing an advantage for real-time shape sensing of curvilinear geometries. The high accuracy and practical utility of the iCS8 element is demonstrated for different cylindrical marine structures through examining coarse iCS8 discretizations with dense and sparse sensor deployments.