We report angle-resolved photoemission spectroscopy (ARPES) results of A-site ordered perovskite CaCu$_3$Ti$_4$O$_{12}$. We have observed the clear band dispersions, which are shifted to the higher energy by 1.7 eV and show the band narrowing around 2 eV in comparison with the local density approximation calculations. In addition, the high energy multiplet structures of Cu 3$d^8$ final-states have been found around 8 - 13 eV. These results reveal that CaCu$_3$Ti$_4$O$_{12}$ is a Mott-type insulator caused by the strong correlation effects of the Cu 3$d$ electrons well hybridized with O 2$p$ states. Unexpectedly, there exist a very small spectral weight at the Fermi level in the insulator phase, indicating the existence of isolated metallic states.
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