Metalens is one of the most prominent applications among metasurfaces since it gives possibilities to replace the conventional lenses for compactness and multi-functionalities. Recently, many studies have been demonstrated to overcome the aberrations of the metalenses for high performance practical applications. Previous studies have used the methods that control the dispersion of meta-atoms for correcting chromatic aberrations and use doublet platform for correcting monochromatic aberrations. Despite these studies and the large demands for simultaneous correction of the aberrations in high numerical aperture metalens, the simultaneous correction has not been demonstrated yet. In this paper, we report the doublet metalens design with high numerical aperture which corrects longitudinal chromatic aberration and four monochromatic aberrations including spherical aberration, coma, astigmatism, and field curvature simultaneously for the three primary visible colors. Based on the novel doublet platform, the multi-wavelength targeted correction lens and geometric phase lens with color filtering functionality are utilized. Our doublet metalens has numerical apertures of 0.33, 0.38, and 0.47 for 445 nm, 532 nm, and 660 nm, respectively. The back focal length of our doublet metalens remains nearly 360 µm for target wavelengths and incident angles up to 30 degrees.