The present invention relates to a carbon fiber-reinforced composite material having a high toughness against delamination, which is prepared by regulating the rate of cure reaction of a thermosetting resin used as a matrix and the rate of dissolving a toughening agent in the matrix to form a morphology gradient depending on a concentration gradient of the toughening agent between layers of the carbon composite material. A process for preparing the carbon fiber-reinforced composite material which comprises the steps of: obtaining a thermosetting resin in a melted or solution form, and adding a catalyst of the thermosetting resin to obtain a prepreg; adding a toughening agent between plies within the prepreg thus impregnated, in a form of film having a uniform thickness or in a form of powder having a uniform distribution; and, curing under a proper reaction temperature and pressure, by autoclave vacuum bag molding method or compression molding method. The carbon fiber-reinforced composite material of the invention has a higher toughness against delamination than the conventional ones, and still has a thermostability and a chemical resistance to solvent or acid which is one of advantages of a thermosetting matrix, while improving a weight penalty phenomenon which is a disadvantage of a conventional interleaved system.