This study examines the growth of tropical cyclone (TC) intensity forecast errors and related intensity predictability for the NOAA operational Hurricane Weather Research and Forecasting (HWRF) model. Using operational intensity forecasts during the 2012 to 2016 seasons, two conditions for a limited range of TC intensity predictability are demonstrated, which include (a) the existence of an intensity error saturation limit, and (b) the dependence of the intensity error growth rate on storm intensity during TC development. By stratifying intensity errors based on different initial intensity bins, it is shown that TC intensity error growth rate is relatively small (∼0.3 kt h−1) at the early stage of TC development, but it quickly increases to ∼1 kt h−1 during TC intensification. Of further importance is that the intensity error saturation varies in the range of 14–18 kt in different ocean basins, thus suggesting the potential dependence of the intensity predictability on large‐scale environment. Additional idealized experiments with the HWRF model confirm the saturation of intensity errors, even under a perfect model scenario. The existence of the intensity error saturation together with the finding of a faster error growth rate for higher intensity suggests that the TC dynamics possesses an inherent limited predictability, which prevents us from reducing the intensity errors in TC dynamical models below a certain threshold.