We report the first results of a near- and mid- infrared deep survey with the Infrared Camera (IRC) onboard AKARI in the performance verification phase. Simultaneous observations by the NIR, MIR-S and MIR-L channels of the IRC with effective integration times of 4529, 4908, and 4417 seconds at 3, 7, and 15 micron, covering 86.0, 70.3, and 77.3 arcmin^2 area, detected 955, 298 and 277 sources, respectively. The 5 sigma detection limits of the survey are 6.0, 31.5 and 71.2 micro Jy and the 50% completeness limit are 24.0, 47.5, and 88.1 micro Jy at 3, 7, and 15 micron, respectively. The observation is limited by source confusion at 3 micron. We have confirmed the turnover in the 15 micron differential source counts around 400 micro Jy, previously detected by surveys with the Infrared Space Observatory. The faint end of 15 micron raw source counts agree with the results from the deep surveys in the GOODS fields carried out with the Spitzer IRS peak up imager and the predictions of current galaxy evolution models. These results indicate that deep surveys with comprehensive wavelength coverage at mid-infrared wavelength are very important to investigate the evolution of infrared galaxies at high redshifts.