$CaMoO_4:Tb^{3+}$ green phosphor powders and thin films were successfully prepared by using the solid-state reaction method and the radio-frequency magnetron sputtering technique, respectively. The crystalline structure of all phosphor powders with different $Tb^{3+}$ ion concentrations was found to be a tetragonal system with the maximum diffraction intensity at $28.58^{circ}$, while that of the phosphor thin films, irrespective of the type of substrate, was amorphous. As for the phosphor powders, the grain particles showed the chain-like patterns with inhomogeneous size distribution, the excitation spectra were composed of a broad band peaked at 307 nm and two small narrow bands centered at 381 and 492 nm, and the highest green emission spectrum was observed at 0.01 mol of $Tb^{3+}$ ions. As for the phosphor thin films, the average transmittance exceeding 85% was measured in the 400~1,100 nm range and the optical band gap showed a significant dependence on the type of substrate.