Ex-situ and in-situ morphological analyses were performed for Cu-phthalocyanine (CuPc) organic semiconductor films by using atomic force microscopy (AFM) and reflection high-energy electron diffraction (RHEED). The focus was the effects of post-annealing on the structural characteristics of CuPc films grown on MgO(001) layers by using an ultra-high-vacuum thermal evaporator. Sphere-to-nanofibril and 2-D to 3-D morphological transitions were observed with increasing CuPc thickness beyond 3 nm. The surface morphology and the crystallinity were drastically improved after an additional cooling of the post-annealed CuPc films thinner than 3 nm. Our results highlight that molecular orientation and structural ordering can be effectively controlled by using different temperature treatments and a proper combination of material, film thickness, and substrate.