The proper design principles are essential for the efficient development of superionic conductors. However, the existing design principles are mainly proposed from the perspective of crystal structures. In this work, the face-centered cubic (fcc) anion frameworks were creatively constructed to study the effects of anion charge and anion volume on the stability of lithium ion occupation and lithium ion migration. Both the large negative anion charges and large anion volumes would increase the relative stabilities of lithium-anion tetrahedron, and Li ions prefer to occupy the tetrahedral sites. For a tetrahedral Li ion migration to adjacent tetrahedral site through an octahedral site, the smaller the negative anion charge is, the lower the lithium ion migration barrier will be. While for an octahedral Li ion migration to adjacent octahedral site through a tetrahedral site, the larger negative anion charge is, the lower the lithium ion migration barrier will be. Our anion framework model can be used for screening superionic conductors, along with the structure and Bader charge information in the AFLOW material database. In addition, new design principles for developing superionic conductors were proposed based on the analyses of the fcc anion framework model. Low Li ion migration enthalpies would be achieved by adjusting the non-lithium elements within the same crystal structure framework to obtain the desired electronegativity difference between the anion element and non-lithium cation element.