High power widely tunable green lasers have potential applications in many fields such as biomedical, lidar, laser spectroscopy, laser display, underwater wireless optical communication, fine processing of nonferrous metals, and so on. Vertical-external-cavity surface-emitting lasers, also known as semiconductor disk lasers, have the advantages of high power, good beam quality and wide bandwidth of gain medium. In this paper, a gain chip with reverse-growth epitaxy structure and emitting wavelength of 1018 nm is designed. A bandwidth of 74 nm above the reflectivity of greater than 99.1 % in the DBR reflection spectrum is obtained, which lays a solid foundation for the realization of high-power widely tunable output. The laser cavity combines a 1018 nm semiconductor gain chip, a folded mirror, and a plane mirror to construct a compact V-shaped resonant cavity. A class I phase-matched LBO nonlinear crystal with a length of 10 mm is placed at the beam waist of the cavity to realize a highly efficient frequency doubling process to produce 509 nm green laser. To meet the requirement of the polarization during frequency conversion and to tune the oscillating wavelength of the laser, a birefringent filter (BRF) is employed in the laser resonant cavity. When the thickness of the used BRF is 1 mm, the obtained wavelength tuning ranges of the fundamental laser and the frequency doubled green laser are 47.1 nm and 20.1 nm, respectively, showing a good tuning capability of the laser. The laser's performance varies with the different thickness of the BRF. When using a 2 mm BRF, a maximum output power of the frequency-doubled green laser of 8.23 W is achieved during continuous tuning, indicating an ideal compatibility of wide tuning characteristics and a high output power. Meanwhile, its beam quality M² factors are 1.00 and 1.03 in the x and y directions, respectively, demonstrating a near diffraction-limited excellent beam quality. This green laser also possesses a frequency doubling conversion efficiency of up to 68.2 %, which enables efficient conversion of the fundamental laser into the frequency doubled green laser. The optical-to-optical conversion efficiency from the absorbed pump light to the frequency-doubled green light also reaches 16.6 %. Meanwhile, the spectral linewidths of the green lasers under different thicknesses of BRFs are found that the thicker the BRF, the narrower the laser line widths, which is consistent with the theoretical results.