Due to its unique properties of nondiffracting propagation, highly-localized intensity distribution, small beam cross-section, and self-healing, a nondiffracting beam is attractive for materials processing, microscopy, and optical research. Various methods have been investigated to generate such beams with conventional optics. However, the transverse size of those nondiffracting beams is restricted by the diffraction-limit. To overcome the diffraction limit, we use the concepts of super-oscillation and the vectorial angular spectrum method to design a phase mask mirror with a focal length of 1 m, radius of 5 mm, and numerical aperture of about 0.005 for a wavelength of 632.8 nm. The phase mask mirror was created with a phase spatial light modulator. Under the illumination of a linearly polarized Gaussian wave, a nondiffracting beam was created with sub-diffraction transverse size. The maximum transverse size of the beam is smaller than the diffraction limit of 0.5λ/NA for a propagation distance greater than 43.3 mm. A nondiffracting beam with smaller transverse size can be realized by further increasing the NA value.