The propargyl radical plays a critical role in various chemical processes, including hydrocarbon combustion, flame synthesis, and interstellar chemistry. Its unique stability arises from the delocalization of π-electrons, allowing it to participate in a wide range of reactions despite being a radical. The self-reaction of propargyl radicals is a fundamental step in synthesizing polycyclic aromatic hydrocarbons. In this work, therefore, a computational study into the C3H3 + C3H3 potential energy surface has been carefully characterized. The calculated results indicate that the reaction can occur by H-abstraction or addition of two propargyl radicals together. The H-abstraction mechanism can create the products P3 (H2CCC + H3CCCH) and P4 (H2CCCH2 + HCCCH) but the energy barriers of the two H-abstraction channels are very high (from 12 to 22kcal/mol). In contrast, the addition mechanism of two propargyl radicals forming the intermediates (I1, I5, I12) and the bimolecular products (P1, P2, P7, P11, P12) are dominant. Among the bimolecular products, the P11 (C6H4 + H2) product is the most energetically favorable, and the channel leading to this product is also the most preferred path compared to all other paths throughout the PES. The calculated enthalpy changes of various reaction paths in this study are in good agreement with the available literature data, indicating that the CCSD(T) method is suitable for the title reaction. The overall rate constant of the reaction depends on both temperature and pressure, reducing with temperature but rising with pressure. The calculated results agree closely with the available experimental values and previous calculated data. Thus, it can be affirmed that in addition to the CASPT2 method as applied in the study of Georgievskii et al. (Phys. Chem. Chem. Phys., 2007, 9, 4259-4268), the CCSD(T) method is also very good for the self-reaction of two propargyl radicals. The M06-2X and CCSD(T) methods with the aug-cc-pVTZ basis set were used to optimize and calculate single-point energies for all species of the reaction. The bimolecular rate constants of the dominant reaction paths were predicted in the temperature and pressure ranges of 300-1800K and 0 - 76,000Torr, respectively, using the VTST and RRKM models with Eckart tunneling correction for the H-shift steps.