Sandwich composite structures are special types of composite in which two stiff facesheets are provided along with a soft core in between. Auxetic honeycomb core sandwich composite structures have an excellent energy absorption capacity, are lighter, stiffer, and have a higher strength-to-weight ratio. In this paper, the nonlinear bending analysis is carried out for sandwich beams having curvilinear fiber facesheets and auxetic honeycomb core. A first-order shear deformation theory (FSDT) is employed in the framework of finite element formulation. The facesheets are made of variable stiffness composite laminate (VSCL) sheets. To produce a VSCL, the fiber orientation is varied continuously across each layer. In constant stiffness composite laminate, the fiber orientation is kept constant throughout the layer. Geometrical nonlinearity is considered as per the von Kármán strain–displacement equations. The Newton–Raphson iteration method is used to solve the nonlinear equations. The study is performed with various facesheet–core arrangements and boundary conditions.