We study experimentally the three-body Coulomb explosion dynamics of carbon dioxide dimer \rm(CO_2)_2^4+ ions produced by intense femtosecond laser field. The three-dimensional momentum vectors as well as kinetic energy are measured for the correlated fragmental ions in a cold-target recoil-ion momentum spectrometer (COLTRIMS). Carbon dioxide dimer is produced during the supersonic expansion of \rm(CO_2)_2 gas from a 30 μm nozzle with 10 bar backing pressure. The linearly polarized laser pulses with a pulse duration (full width at half maximum of the peak intensity) of 25 fs, a central wavelength of 790 nm, a repetition rate of 10 kHz, and peak laser intensities on the order of \rm8 \times10^14\;\rmW/cm^2 are produced by a femtosecond Ti:sapphire multipass amplification system. We concentrate on the three-particle breakup channel \rm(CO_2)_2^4+ \rightarrow \rmCO_2^2++\rmCO^++ \rmO^+. The two-particle breakup channels, \rm(CO_2)_2^4+ \rightarrow \rmCO_2^2++ \rmCO_2^2+ and \rmCO_2^2+\rightarrow CO^++O^+, are selected as well for reference. The fragmental ions are guided by a homogenous electric field of 60 V/cm toward microchannel plates position-sensitive detector. The time of flight (TOF) and position of the fragmental ions are recorded to reconstruct their three-dimensional momenta. By designing some constraints to filter the experimental data, we select the data from different dissociative channels. The results demonstrate that the three-body Coulomb explosion of \rm(CO_2)_2^4+ ions break into \rmCO_2^2++\rmCO^++\rmO^+ through two mechanisms: sequential fragmentation and non-sequential fragmentation, in which the sequential fragmentation channel is dominant. These three fragmental ions are produced almost instantaneously in a single dynamic process for the non-sequential fragmentation channel but stepwise for the sequential fragmentation. In the first step, the weak van der Waals bond breaks, \rm(CO_2)_2^4+ dissociates into two \rmCO_2^2+ ions; and then one of the C=O covalent bonds of \rmCO_2^2+ breaks up, the \rmCO_2^2+ ion breaks into \rmCO^+ and \rmO^+. The time interval between the two steps is longer than the rotational period of the intermediate \rmCO_2^2+ ions, which is demonstrated by the circle structure exhibited in the Newton diagram. We find that the sequential fragmentation channel plays a dominant role in the three-body Coulomb explosion of \rm(CO_2)_2^4+ ions in comparison of the event ratio of the two fragmentation channels.