Biological invasions are a global threat to community structure and biodiversity, and it is therefore necessary to understand the fundamental mechanisms of biological invasions. The success of a biological invasion is not only related to the biology and ecological characteristics of the invaders, but it also depends on the invaded community's vulnerability. A number of experiments have shown that parasitism affects biological invasion both directly and indirectly, but how these two key redistribution processes of biological invasion and disease emergence are interlinked is a relatively new research topic. In this study, we used a cellular automata simulation model to explore how the indirect effects of parasitism (including density-mediated effects and trait-mediated effects) influence the spatial invasion dynamics of an exotic predator. In the spatial model, the native species and invasive species form an intraguild predation with their basal resource. First, we explored the spatial distribution patterns of the native and invader species with and without parasite-mediated effects. Overall, the distribution patterns formed spatial traveling waves. Along the spatial wave from the front to the back, the susceptible native prey was first followed by the infected ones, then by the susceptible invader predators, and finally by the infected invader predators. Due to host-parasite and predator-prey interactions, the parasites have to encircle susceptible hosts for their possible survival, whereas the predators need to chase after the prey for survival. Second, three main coexistence results were obtained under different parasite effects: invade successfully, coexist with local species, and invade unsuccessfully. We mainly focused on the effects of the exotic predator's predatory rate on native prey parameters (λ₁₂) and the intraspecific infection rate (ββ) on the invasion of invader predator species. Without parasites, the exotic predator can invade successfully and quickly by increasing λ₁₂, whereas the coexistence region for invasive predator and native prey species is very small. However, the coexistence region expands remarkably when parasites are present. Furthermore, the impact of trait-mediated indirect effects on the invasion of predator species was more dramatic than density-mediated effects. Moreover, the coexistence region was the largest when hosts were affected by density and trait effects simultaneously, causing the density and trait effects together to have the largest inhibiting effect on invasion. In addition, the influence of transmission rate ββ on the dynamics of alien invasions was affected by these indirect effects. In the scenarios with density and trait-mediated effects together, as well as with density-only effects, the invader became extinct as parameter ββ increased to some thresholds. However, when modeling just trait-only effects, the invasion predators did not go extinct, but coexisted steadily with the native prey species. Overall, from the model, we identified conditions that inhibit exotic invasions by introducing parasites as a biological control. Our research can therefore contribute to the development of biological invasion theories, and provide a basis for the prevention and control strategies to handle biological invasions.