In this paper, we propose a nanoscale Infrared Plasmonic Perfect Absorber (IPPA) based on Metal-Insulator-Metal (MIM) structure with two different nano- apertures in the upper metal layer for sensing the refractive index of liquids (analyte), and use the 3D FDTD numerical method in order to obtain the absorption spectrum of each structure for perpendicular incidence of a plane wave light within 1500–1850 nm wavelength range. Simulation results show that, a resonance peak is obtained in each spectrum. When the analyte refractive index increases, the resonance peak have a red shift. Once, in nano-aperture design by rectangular branches, FWHM and Figure of Merit (FOM) of resonance peak were obtained, 89.50 and 2.91, respectively. Also, in nano-aperture design by sharp tip triangular branches, FWHM and FOM of resonance peak were obtained, 57.98 and 3.04, respectively. The analysis of electromagnetic fields show that, the field localization at the tips of the aperture branches increases, and the bandwidth of the resonance peak is reduced. Hence, the achieved FOMs are very suitable for different liquids sensing with refractive indices close to each other in a narrow-band spectral range.