Magnetic refrigeration (MR) based on the magnetocaloric effect (MCE) has been recognized as an environmentally benign and energy-efficient cooling technology. Exploring suitable magnetocaloric materials is a crucial prerequisite for practical MR applications. We have herein provided a systematic investigation of the crystal structure, microstructure, electronic structure, magnetic phase transition, critical behavior, and MCE of the GdCoC compound featuring excellent cryogenic magnetocaloric performance by means of experimental determination and theoretical calculation. The GdCoC compound is crystallized in a simple layered tetragonal crystal structure with a P42/mmc space group and undergoes two successive ferromagnetic (FM) transitions along with a low-temperature weak antiferromagnetic (AFM) transition under low magnetic fields. Density functional theory calculations confirms the FM coupling of the Gd and Co intra-sublattice interactions, whereas AFM coupling for their inter-sublattice interaction. The magnetic transitions are merged in to one under high magnetic fields which has been confirmed to be second-order type and its critical behavior can be understood in the framework of tri-critical mean-field model, whereas the low-temperature weak AFM transition is belonging to the first-order type. The excellent magnetocaloric performance of the GdCoC compound was identified by the parameters of magnetic entropy change, adiabatic temperature change, temperature-averaged entropy change, relative cooling power, and refrigerant capacity, which are superior to most of the well-known magnetocaloric materials with similar working temperatures, making it attractive for practical cryogenic MR applications.