Two-dimensional material gallium selenide (GaSe) films were grown on sapphire, gallium nitride and gallium arsenide substrates by molecular beam epitaxy. The optical properties of GaSe films were analyzed by the Raman spectroscopy. The Effects of growth conditions, different substrate temperatures, Se/Ga flux ratio and epitaxial time, on the epitaxial morphology and Raman spectrum were studied. The pyramidal structure of GaSe indicates that its growth mechanism is layer-by-layer growth. A structure change, from pyramid to closed-loop triangular structure, with the increasing epitaxial time was observed. The closed-loop triangular structure is caused by the concentric multilayer growth, which accompanies a lift of the GaSe E_2g^1 mode degeneracy in the Raman spectrum. It implies the presence of in-plane stress, which results in the change of growth mechanism of GaSe.