In the field of ecology, habitat loss and fragmentation are the two main characteristic forms of habitat destruction and the main drivers of species extinction, resulting in the gradual loss of biodiversity. So far, many scholars have made some progress in the theoretical research of the spatial food web, but research on the effect of introducing an invasive species in an omnivorous food web is very rare. In order to explore the impact of invader on the persistence of species in omnivorous food webs, we constructed a model framework to describe the patch occupation of each species in omnivorous systems. Our model results show that invasive species is a prey of species in omnivorous food webs is easier to invade than invasive species is a predator of species in original omnivorous food webs on habitat loss and fragmentation. One conclusion also can be drawn is that when an invasive species is a prey of species in omnivorous food webs, no matter what trophic level the invasive species is invade, it is more successful. But when invasive species is a predator of species in different trophic levels on omnivorous food webs, they show different coexistence patterns. The invasion of a species has little effect upon the stability of original omnivorous food web for habitat loss and fragmentation, and will only make the original omnivorous food web more stable and more complicated. Therefore, we have proved that the omnivorous food web is stable and is not easy to destroy this ecological fact. Some examples to illustrate the reliability of our model results are discussed.