The coupled nonlinear Schr?dinger equation was used as a theoretical model to study the interaction of two first-order dark rogue waves in a normal dispersion single-mode fiber. Based on the exact solution of first-order dark rogue wave, the interaction between two adjacent first-order dark rogue waves is discussed in terms of spacing, phase and ratio of amplitude coefficients using split-step Fourier numerical simulation. Based on the exact solution of the second-order dark rogue wave, the nonlinear interaction of two first-order dark rogue waves is discussed.The results show that the interaction of two adjacent in-phase first-order dark rogue waves will generate "twisted" dark rogue waves when the interval parameter T₁ is 0, 5, 20. Compared to the energy diffusion of a single dark rogue wave, the "twisted" dark rogue wave can split and form multiple secondary dark rogue waves.In the case of out of-phase, when the interval parameter T₁ is 2, 7, 12, the interaction of two adjacent first-order dark rogue waves can also stimulate and generatethe "twisted" dark rogue waves. And the initially excited spatial position of the "twisted" dark rogue wave deviates from that of the original single dark rogue wave.The larger the ratio of amplitude coefficients, the closer this spatial position is to 5.Second-order dark rogue waves can be regarded as the nonlinear superposition of two first-order dark rogue waves.The composite and three-component second-order dark rogue waves are slightly similar to the interaction between two adjacent first-order dark rogue waves.