The existing analytical solution for the problem of the heat-transfer-controlled growth of a spherical vapor bubble moving with a constant velocity under the assumptions of a thin thermal boundary layer and potential flow results in a complicated integral equation for the bubble radius and is too unwieldy to be used in multiphase flow models. The goal of this work is to suggest for this problem an approximate solution that gives correct asymptotic behavior and yields a simpler expression for the bubble growth rate. Comparison with the exact solution showed that this way a good approximation can be obtained.