Detailed spectral structures in the low-temperature photoluminescence (3.5 K) of an InAlAs random alloy grown by molecular beam epitaxy on an InP substrate were studied, with three clearly distinguished emission peaks. Based on the temperature-dependent photoluminescence measurements, the two peaks at 1.5404 and 1.5229 eV are localized state emissions, and the one at 1.4916 eV is likely caused by longitudinal optical (LO) phonon replica. The peak assignments are also supported by excitation intensity-dependent photoluminescence spectrum and Raman spectrum measurements. The peak at 1.5229 eV shows a strongly localized behavior evidenced by the typical inverted S-shaped variation of the peak position with respect to increased temperatures which can be well described by the localized-state ensemble (LSE) model. A localization energy of around 19.8 meV is determined for the 1.5229 eV emission at 3.5 K. The temporal behaviors of these emissions at 3.5 K were also discussed based on the time-resolved photoluminescence spectra. The findings here unveil the characteristics of the localized states in the InAlAs alloy and may be useful for developing optoelectronic devices in the near IR region.