This work analyzed experimental and numerically the growth kinetics of β´precipitation of a Cu4wt.%Ti alloy after aging at 400, 500 and 600 °C for times from 0.0166 h to 200 h. Results indicated that the precipitation process is almost controlled by nucleation and growth during aging at 400 °C, originating a slow growth kinetics of precipitation. In contrast, the coarsening of precipitates dominates the precipitation process during aging at 500 and 600 °C. The interfacial energy of interface between the a matrix phase and β´ precipitates was determined to be about 0.1135, 0.0980 and 0.0725 Jm -2 for aging at 400, 500 and 600 °C, respectively. These values suggest a coherent interface which is in agreement with the flat faces of β´ cuboid precipitates. Calculated Time-Temperature-Precipitation diagram for the β´ precipitation indicated good agreement with experimental results. Precipitation hardening was higher for the slower growth kinetics of precipitation.