We present rest-frame optical/near-infrared spectra of the gravitationally lense d quasar APM 08279+5255 at $z=3.91$ that has been taken using the Infrared Camera (IRC) onboard the AKARI infrared satellite. The observed continuum consists of two components; a power-law component dominating optical wavelengths which is the direct light from the central source and thermal emission dominating near-infrared wavelengths which is attributed to the emission from hot dust in the circumnuclear region. The thermal emission well represents optically thick emission by hot dust at T ~ 1300K with tau(2micron)> 2 and apparent mass, M(hot) >10 M_sun. Thus, our observations directly detected the optically thick region of hot dust in APM 08279+5255. HI recombination lines of H_alpha(0.656micron), Pa_alpha(1.875micron), and Pa_beta(1.282micron) are clearly detected at 3.2, 6.3, and 9.3 micron. Simulations with the photoionization models suggest that APM 08279+5255 has BLR(Broad Line Region) clouds characterized by log n_{H} ~ 12- 14 for the gas density, log U ~ -2 - -6$ for the ionization parameter, and E(B-V) ~ 0.3-0.6$for the broad line region. Thus, optically thick emission of hot dust support an idea on non-spherical distribution of dust near the central source, consistent with the Active Galactic Nuclei model with the dust torus. The temperature of hot dust and flux ratios of these HI lines are similar to those observed in low-redshift quasars. There are significant time-variations in the HI lines, which are probably caused by variations in the brightness of the central source.