This study provides a numerical scheme for solving nonlinear third-kind Volterra delay integral equations (VDIEs) using mesh-free approaches based on the collocation technique with radial basis functions (RBFs). The proposed approach is stable and requires less computer memory. It combines RBFs and a collocation method technique based on scattered points to represent the solution of third-kind VDIEs by interpolating RBFs using Legendre-Gauss–Lobatto nodes and weights. A description of the approach to the suggested equations is presented. Furthermore, the error analysis of the proposed scheme is investigated. A numerical example that clearly illustrates the validity of the proposed scheme is presented. This problem was also compared with the moving least squares collocation technique and other methods, demonstrating the reliability and efficiency of this approach for solving third-kind VDIEs.