We demonstrate the full vectorial feature of second-harmonic generation (SHG), i.e., from infrared full Poincaré beams to visible full Poincaré beams, based on two cascading type I phase-matching beta barium borate crystals of orthogonal optical axes. We visualize the structured features of the vectorial SHG wave by using Stokes polarimetry and show the interesting doubling effect of the polarization topological index, i.e., a low-order full Poincaré beam is converted to a high-order one. However, the polarization singularities of both C points and L lines are found to keep invariant during the SHG process. Our scheme could offer a deeper understanding on the interaction of vectorial light fields with media and can be generalized to other nonlinear optical effects.