We present two bright galaxy candidates at z ∼ 13 identified in our H-dropout Lyman break selection with 2.3 deg 2 near-infrared deep imaging data. These galaxy candidates, selected after careful screening of foreground interlopers, have spectral energy distributions showing a sharp discontinuity around 1.7 µm, a flat continuum at 2−5 µm, and non-detections at < 1.2 µm in the available photometric datasets, all of which are consistent with a z ∼ 13 galaxy. An ALMA program targeting one of the candidates shows a tentative 4σ [Oiii]88µm line at z = 13.27, in agreement with its photometric redshift estimate. The number density of the z ∼ 13 candidates is comparable to that of bright z ∼ 10 galaxies, and is consistent with a recently proposed double power-law luminosity function rather than the Schechter function, indicating little evolution in the abundance of bright galaxies from z ∼ 4 to 13. Comparisons with theoretical models show that the models cannot reproduce the bright end of rest-frame ultraviolet luminosity functions at z ∼ 10 − 13. Combined with recent studies reporting similarly bright galaxies at z ∼ 9 − 11 and mature stellar populations at z ∼ 6 − 9, our results indicate the existence of a number of star-forming galaxies at z > 10, which will be detected with upcoming space missions such as James Webb Space Telescope, Nancy Grace Roman Space Telescope, and GREX-PLUS.