The half-metallic ferromagnets are likely materials to the spintronics systems for the next generation electronic devices. Among the half-metallic ferromagnetic materials, the equiatomic quaternary Heusler (EQH) compounds get great attention in the recent times. In this study, the EQH CoXCrAl (X = V, Nb, and Ta) compounds are investigated using Density Functional Theory (DFT). The three structural types as type-I, type-II, and type-III, are considered to determine the most stable structural types of CoXCrAl compounds. Furthermore, the three magnetic configurations as paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM), are studied to find out the most stable magnetic configuration. The type-I FM configuration is the most stable configuration for the CoXCrAl compounds. The calculated electronic band structures reveal that the CoXCrAl compounds are halfmetals with metallic behavior in spin-up channel and semiconducting behavior in spin-down channel. Also, the possible d-d hybridizations between the Co, X, and Cr atoms are investigated to show the half-metallic character in detail. Furthermore, the calculated elastic constants satisfy the Born stability criteria, then the CoXCrAl compounds have mechanical stability. Using the determined constants, the mechanical properties are obtained for CoXCrAl compounds. In addition, the dynamical properties are studied and it is found that CoXCrAl compounds are dynamically stable. The structural, magnetic, electronic, mechanic and dynamical properties of CoXCrAl compounds that are the potential candidates for the spintronics applications are presented in this study.