The normal zone propagation velocity is an important feature in the design of a superconducting magnet. In the particular case of the ATLAS-Barrel toroid coil protection, it is all the more important as the fast discharge is essentially realized through the toroid windings by exciting quench heaters. The time constant of that fast discharge, and consequently the final magnet temperature, are therefore determined by the heaters activation time constant and the quench propagation kinetics. Taking into account the particular Race-track shape of the ATLAS-Barrel coil, the transverse quench propagation dominates the duration of the fast discharge. In this paper, we present, at first, the experimental measurements of the transverse normal zone propagation velocities made at CERN in 2002 on the B0 model-coil up to a maximal 24 kA operating current. Then, we present a code developed in our laboratory, based upon CAST3M finite-element code, which allows the computation, among others, of the transverse normal zone propagation velocities. We finally compare computation and experimental results and obtain a very satisfactory agreement in a large (15-24kA) operating current range.