The precision casting method based on alumina-based ceramic cores is one of the main techniques used to manufacture hollow turbine blades. Additive manufacturing (AM) technology provides an alternate solution to fabricating ceramic cores quickly and precisely. As the complexity of the structure increases and the strength of the material improves, the leaching process of the cores becomes more complicated. This study proposes a compound pore-forming method to increase the porosity of ceramic cores by adding a preformed-pore agent and materials that convert to easy-to-corrode phases. The preformed-pore agents (e.g., carbon fibers) can be burned off during sintering to form pores before the leaching, and the easy-to-corrode phases (e.g., CaCO3, SiO2, β-Al2O3) can be leached firstly to form pores during the leaching process. The pores formed in the aforementioned two stages increase the contact area of the cores and leaching solution, thus improving the leaching rate. In the current study, the additive amount of the preformed-pore agent was optimized, and the effect of the easy-to-corrode phases on the comprehensive properties of the cores was then compared. Based on this, the corresponding model was established.