We report on infrared imaging observations of the z = 2.429 radio galaxy B3 0731+438 with the Subaru telescope. The images were taken with the K′-band filter and the 2.25 μm narrow-band filter to examine the structure and properties of the Hα+[NII] λλ 6548, 6583 emission-line components. The Hα+[NII] emission-line image shows biconical lobes with an extent of 40 kpc, which are aligned with the radio axis. The rest-frame equivalent widths of the emission lines at these cones are as large as 1100 Å, and can be well explained by a gas-cloud model photoionized by power-law continuum radiation. The isotropic ionizing photon luminosity necessary to ionize the hydrogen gas in these cones amounts to 1057 (photons s-1), which is larger than that in the majority of radio-loud QSOs. From these results, we propose that the Ha alignment effect in this object is produced by biconical gas clouds, which are swept up by the passage of radio jets, and are ionized by strong UV radiation from a hidden AGN. The continuum image consists of two components, a stellar-like point source and an extended diffuse galaxy. These are supposed to be a type-2 AGN and its host galaxy. The SED is fitted by a combination of spectra of a reddened dust-scattered AGN and an instantaneous starburst population of 500 Myr old. The stellar mass of the galaxy is estimated to be 3 × 1011 M(fisheye) , which is as large as that of typical 3C radio galaxies at z = 1.