The generalized gradient approximation (GGA) method based on density functional theory (DFT) was used to analyze the structural stability and electronic properties of the unconventional carbon halogen fullerenes C56X10(X=F, Cl, Br, I). The investigation of structural stability indicates that the evolution of energy gaps, the reactive heat (△E), the maximal vibration frequencies, and the minimal vibration frequencies of C56X10(X=F, Cl, Br, I) all decrease with an increase in the atomic number of X. This indicates that the stabilities should decrease from C56F10 to C56I10. C56F10 is the most stable molecule among the four molecules and we predict that it can be isolated and synthesized because of the successful isolation of C56Cl10. From the analysis of the frontier orbitals of C56 and C56X10(X=F, Cl, Br, I), the C atoms are located at the abutting penta n sites and both the hexa n-hexa n-penta n vertex functions are the most active sites on C56 and this is suitable for halogen atom attachment. Our calculations also show that the electronegativity of C56X10(X=F, Cl, Br, I) cluster molecules decrease with an increase in the atomic number of X. However, the electronegativity of the C—X fragment in the molecules is affected by its location.