The non-ferrous shape memory alloys have, normally, two problems that hinder its use in industrial scale: the natural aging and grains growth. The first degrades the memory effect, while the second, observed during the processing of alloy, modifies the temperatures which the transformations occur. Thus, the study of kynetic of recrystallization is important for enabling the control of hardened state in function of treatment time, without causing excessive grain growth. Therefore, the objective of this study is to determine the kinetics of recrystallization of Cu-14Al-4Ni shape memory alloy, based on an empirical law of the formation of Jonhson-Mehl-Avrami, as well as their activation energies for grain growth process according to the empirical Arrhenius law. The alloy was vacuum melted in an induction furnace. After casting, the bulk samples of the alloy were homogenized for 24 hours, solubilized and hot rolled followed by water-quenching to initiate the recrystallization. Then, different samples were annealed at temperatures close to the peak, start and end of the DSC curve. Following the heat treatments, the samples were submitted to mechanical tests and the values of the properties were correlated to the fraction transformed for determination of recrystallization’s kinetic. For the characterization of the grain growth process, analyses in optical microscopy were accomplished and all annealed samples were examined by statistical metallography and the grain sizes were measured. After measurements, the ln[-ln(1-Y rec )] x ln(t) and the ln [D-D o ] x 1/T diagrams were plotted to determine the parameters of Jonhson-Mehl-Avrami equation and the activation energy of the process, respectively. The results showed that the equation of the recrystallized fraction follows the empiric law of the formation of Jonhson-Mehl-Avrami for the considered property, as well as, also showed that the alloy Cu-14Al-4Ni is extremely sensitive to temperature variation in which the alloy is treated, having a dual kinetics of grain growth. In the first domain, between 670 and 710°C, the diagram provides a value for the activation energy equal to 39.32 KJ/mol, in the second domain, between 710 and 790°C, the diagram provides a value for the activation energy equal to 9.01 KJ/mol.