A novel four-layer functionally graded fiber-reinforced cementitious composite (FGFRCC) as a beam component has been fabricated using extrusion and pressing techniques. The FGFRCC features a linear gradation of fiber volume fraction through the beam depth. The bending test shows the enhanced bending strength of the FGFRCC without delamination at layer interface. Microstructure investigation verifies the fiber gradation and the smooth transition between homogeneous layers. The remaining part of the study is the development of a hybrid technique for the extraction of mode I cohesive zone model (CZM). First, a full-field digital image correlation (DIC) technique has been adopted to compute the two-dimensional displacement fields. Such displacement fields are used as the input to the finite element (FE) formulation of an inverse problem for computing the CZM. The CZM is parameterized using flexible splines without assumption of the model shape. The Nelder-Mead optimization method is used to solve the ill-posed nonlinear inverse problem. Barrier and regularization terms are incorporated in the objective function for the inverse problem to assist optimization. Numerical tests show the robustness of the technique and the tolerance to experimental noise. The techniques are then applied to plastics and homogeneous FRCCs to demonstrate its broader application.