In this work, we have investigated the structural, mechanical, electronic, thermal, vibrational, and optical properties of a new MAB phase Cr4AlB4 for the first time within the framework of density functional theory (DFT) and compared with other MAB phases, Cr2AlB2 and Cr4AlB6. The computed lattice constants are in excellent agreement with the available experimental as well as theoretical values. The new compound is found to be mechanically and dynamically stable as evident from the calculated elastic properties and phonon dispersion spectra. From the theoretical analysis of Pugh’s ratio, Poisson’s ratio, and Cauchy pressure, all the MAB compounds studied here are brittle in nature. The calculated hardness of the studied MAB compounds shows good agreement with the available measured values for other MAB phases. The synthesized Cr4AlB4 is expected to be a material of high potentials for use in hypersonic vehicles, scramjet engines, and thermal management electronics as it possesses high bulk modulus, high stiffness constants, high Debye temperature, as well as high thermal conductivity. The calculated electronic band structures reveal the metallic characteristics of the studied MAB phases. The electron density of states suggests that the chemical bonding is a mixture of covalent, metallic and polar covalent in nature. The optical reflectivity suggests that the studied MAB compounds are promising materials for protection against solar heating. Temperature and pressure dependent thermal properties are investigated through quasi-harmonic Debye model for the first time. The present results might be complementary data for future experimental and theoretical works.