The crossing dynamics at an entanglement point of surfactant threadlike micelles in an aqueous solution was studied using a mesoscopic simulation method, dissipative particle dynamics, with a coarse-grained surfactant model. The possibility of a phantom crossing, which is the relaxation mechanism for the pronounced viscoelastic behavior of surfactant threadlike micellar solution, was investigated. When two threadlike micelles were encountered at an entanglement point under the condition close to thermal equilibrium, they fused to form a four-armed branch point. Then, a phantom crossing reaction occurred occasionally, or one micelle was cut down at the branch point. Increasing the repulsive forces between hydrophilic parts of the surfactants, fusion occurred less and the threadlike micelle was frequently broken down at an entanglement point. In these three schemes (a phantom crossing cut down at the branch point, and break down at the entanglement point), the breakage occurs at somewhere along the threadlike micelle. The breakage is considered as an essential process in the relaxation mechanism, and a phantom crossing can be seen as a special case of these processes. To explain the experimental evidence that a terminal of threadlike micelles is scarcely observed, a mechanism was also proposed where the generated terminal merges into the connected micelle part between two entanglement points due to the thermal motion.