We experimentally studied the three-body fragmentation dynamics of CO(2) initiated by intense femtosecond laser pulses. Sequential and nonsequential fragmentations were precisely separated and identified for CO(2)(3+) to break up into O(+) + C(+) + O(+) ions. With accurate measurements of three-dimensional momentum vectors of the correlated atomic ions and calculations of the high-level ab initio potential of CO(2)(3+), we reconstructed the geometric structure of CO(2)(3+) before fragmentation, which turns out to be very close to that of the neutral CO(2) molecule before laser irradiation. Our study indicated that Coulomb explosion is a promising approach for imaging geometric structures of polyatomic molecules if the fragmentation dynamics can be clearly clarified and the appropriate dissociation potential is provided for multiply charged molecular ions.