  We present near-infrared spectra of three low-luminosity protostars and one
background star in the Perseus molecular cloud, acquired using the Infrared
Camera (IRC) onboard the \textit{AKARI} space telescope. For the comparison
with different star-forming environments, we also present spectra of the
massive protostar AFGL 7009S, where the protostellar envelope is heated
significantly, and the low-mass protostar RNO 91, which is suspected to be
undergoing an episodic burst. We detected ice absorption features of \ch{H2O},
\ch{CO2}, and \ch{CO} at all spectra around the wavelengths of 3.05, 4.27, and
4.67 $\mu$m, respectively. At least two low-luminosity protostars, we also
detected the \ch{XCN} ice feature at 4.62 $\mu$m. The presence of the
crystalline \ch{H2O} ice and \ch{XCN} ice components indicates that the
low-luminosity protostars experienced a hot phase via accretion bursts during
the past mass accretion process. We compared the ice abundances of
low-luminosity protostars with those of the embedded low-mass protostars and
the dense molecular clouds and cores, suggesting that their ice abundances
reflect the strength of prior bursts and the timescale after the last burst.
