A cooldown time is one of the major factors in many cryocooler applications, especially for the design of conduction-cooled superconducting apparatus. The estimation of cooldown seeks the elapsed time to cool thermal object by a cryocooler during initial cooldown process. This procedure includes the dimension of cold mass, heat transfer analysis for cryogenic load and available refrigerating capacity of a cryocooler. This method is applied to the specific cooling system for a 3 Tesla superconducting magnet cooled by a two-stage GM cryocooler. The result is compared with that of experiment, showing that the results of proposed method have a good agreement with experiments during initial cooling of superconducting magnet.