A superfast, multidimensional, and compact pressurized water reactor nodal code, SUPERNOVA (SPNOVA), which is much faster than conventional nodal codes and is very accurate, has been developed at Westinghouse Electric Corporation. A kinetics version of this code, SPNOVA-K, is now developed for applications to three-dimensional core kinetics analysis. The theory involved in the kinetics generalization of SPNOVA is discussed and the performance of SPNOVA-K is described. SPNOVA-K adopts the stiffness confinement method of time variable discretization. This method can provide a very stable solution against the size of the discrete time step, allowing much larger step sizes to be used.