In this work, the growth kinetics of MX (M = metal, X = C/N) nanoprecipitates in type 347H austenitic steel was systematically studied. To investigate the coarsening behavior and the growth mechanism of MX carbonitrides during long-term aging, experiments were performed at 700, 800, 850, and 900°C for different periods (1, 24, 70, and 100 h). The precipitation behavior of carbonitrides in specimens subjected to various aging conditions was explored using carbon replicas and transmission electron microscopy (TEM) observations. The corresponding sizes of MX carbonitrides were measured. The results demonstrates that MX carbonitrides precipitate in type 347H austenitic steel as Nb(C,N). The coarsening rate constant is time-independent; however, an increase in aging temperature results in an increase in coarsening rate of Nb(C,N). The coarsening process was analyzed according to the calculated diffusion activation energy of Nb(C,N). When the aging temperature was 800–900°C, the mean activation energy was 294 kJ·mol−1, and the coarsening behavior was controlled primarily by the diffusion of Nb atoms.