In this study, an extension of the material point method with second-order convected particle domain interpolation (CPDI2) to full integration scheme is proposed. To mitigate the hourglass modes, the proposed full-integration CPDI2 (fCPDI) method employs more than one particle for each element located at the Gauss points of the second-order Gauss-Legendre quadrature. An anti-locking procedure is adopted in the fCPDI method to avoid the volumetric locking caused by over-constraining because of the full integration. Numerical analysis of a two-dimensional bearing capacity problem by the fCPDI method with the anti-locking procedure well reproduces Prandtl’s theoretical solution. Numerical examples of the footing foundation penetration problem demonstrates that the proposed method effectively mitigates the hourglass mode observed in the case using the original CPDI2 method. Coupling the fCPDI method with the generalized interpolation material point (GIMP) method enables to compensate the mesh tangling, which is the weakness of the element-based method, including the CPDI2 and fCPDI methods in large deformation regimes.