In this article, the forming limit diagram (FLD) for aluminum 6061 sheets of thicknesses of 1 mm and 3 mm was determined numerically and experimentally, considering different punch velocities. The punch velocity was adjusted in the range of 20 mm/min to 200 mm/min during the Nakazima test. A finite element (FE) simulation was carried out by applying the Johnson–Cook material model into the ABAQUSTM FE software. In addition, a comparison between the simulation and the experimental results was made. It was observed that by increasing the punch velocity, the FLD also increased for both thicknesses, but the degree of the improvement was different. Based on these results, we found a good agreement between numerical and experimental analyses (about 10% error). Moreover, by increasing the punch velocity from 20 mm/min to 100 mm/min in 1 mm-thick specimens, the corresponding FLD increased by 3.8%, while for 3 mm-thick specimens, this increase was 5.2%; by increasing the punch velocity from 20 mm/min to 200 mm/min in the 3 mm-thick sheets, the corresponding FLD increased by 9.3%.