The 3D printing process of calcia ceramic cores based on slurry extrusion was investigated for precision casting with complex inner cavities. The ceramic slurry was prepared by mixing calcium carbonate powder with polyethylene glycol solution, and ceramic green bodies were prepared using a self-constructed extrusion 3D printing device, followed by a sintering process to obtain ceramic cores for casting. A three-factor, three-level Box-Behnken test was conducted based on the response surface method with needle internal diameter, layer height/internal diameter and printing speed, using the surface roughness of the green bodies as a measure. A stepwise regression method was used to fit a surface accuracy regression model and the optimal process strategy was derived by Analysis of Variance (ANOVA). The results indicate that the inner diameter of the needle is the main factor affecting the accuracy of the ceramic green body. With the optimal 3D printing process parameters, which are 0.41 mm for the needle inner diameter, 0.75 for the ratio of the layer height/needle diameter, and 29.87 mm/s for the printing speed, the surface roughness of the ceramic body is 35.39 μm.