Taking Haixin Bridge as an example, the structural response of a new type arch bridge composed of an inclined arch and a curved beam under cable breaking is analyzed numerically. The cable breaking at different positions, different numbers of broken cables and different ways of breaking are modeled and calculated, and the remaining cables’ internal force and main girder’s deflection are selected as research indexes to evaluate the degree of impact effect of broken cables on the bridge. The numerical results show that (1) duration time of cable breaking is an important factor affecting the impact effect of the bridge, when the cable breaking time is less than 1% of the first order natural vibration period of the structure, the dynamic response caused by cable breaking no longer variates with time; (2) for the cables adjacent to the breaking cable at equal distances, the cable with a shorter length will carry more released force of breaking cable than the longer, and the impact effect is more significant; (3) the dynamic response of displacement and cable force caused by cables at different locations are different, a cable located in the L/4 arch rib area suddenly breaking shows the largest dynamic response; (4) it is feasible to take the dynamic amplification factor (DAF) of cable force and the main girder’s deflection as 2, but it is unsafe to take the DAF of the arch rib’s deflection as 2; (5) the dynamic response of multiple cables breaking at the same time cannot be simplified as a linear superposition of single cable breaks one by one, and the amplification effect becomes more significant with the increase of the number of broken cables. These conclusions can provide guidance for structural safety assessment of similar arch bridges after cable breakage.