Summary: Recently, a new class of semi-Lagrangian methods for the BGK model of the Boltzmann equation has been introduced by G. Russo and F. Filbet [Kinet. Relat. Models 2, No. 1, 231–250 (2009; Zbl 1372.76090)]. These methods work in a satisfactory way either in a rarefied or a fluid regime. Moreover, because of the semi-Lagrangian feature, the stability property is not restricted by the CFL condition. These aspects make them very attractive for practical applications. In this paper, we prove that the discrete solution of the scheme converges in a weighted \(L^1\) norm to the unique smooth solution by deriving an explicit error estimate.