The understanding of pressure-dependent fundamental properties of materials is very essential, not only for basic scientific knowledge but also for advanced technological applications. Experimental observations have fully revealed the hexagonal-to-rocksalt phase transition in the GaSe system under high pressure. In this article we systematically investigate the pressure-induced structural phase transition and related phonon, electronic, and optical properties of hexagonal ε-GaSe through a complete first-principles theoretical framework developed by the density-functional-theory calculations. The study focuses on geometric optimization, electronic band structures, electron localization functions, phonon spectra, dielectric properties, and optical spectra of the GaSe system under hydrostatic pressure. This work also includes an analysis of the phase transformation mechanism using the solid-state nudged elastic band method. Our research sheds light on the physics of structural phase transitions in layered materials and offers potential for the development of pressure-manipulated electronics and optoelectronics.