We demonstrate the lateral optical confinement of GaN-based vertical-cavity surface-emitting lasers (GaN-VCSELs) with a cavity containing a curved mirror that is formed monolithically on a GaN wafer. The output wavelength of the devices is 441-455 nm. The threshold current is 40 mA (Jth = 141 kA/cm2) under pulsed current injection (Wp = 100 ns; duty = 0.2%) at room temperature. We confirm the lateral optical confinement by recording near-field images and investigating the dependence of threshold current on aperture size. The beam profile can be fitted with a Gaussian having a theoretical standard deviation of σ = 0.723 µm, which is significantly smaller than previously reported values for GaN-VCSELs with plane mirrors. Lateral optical confinement with this structure theoretically allows aperture miniaturization to the diffraction limit, resulting in threshold currents far lower than sub-milliamperes. The proposed structure enabled GaN-based VCSELs to be constructed with cavities as long as 28.3 µm, which greatly simplifies the fabrication process owing to longitudinal mode spacings of less than a few nanometers and should help the implementation of these devices in practice.