A branching Lévy process can be seen as the continuous-time version of a branching random walk; see [BM17]. It describes a particle system on the real line in which particles move and reproduce independently one of the others, in a Poissonian manner. Just as for Lévy processes, the law of a branching Lévy process is determined by its characteristic triplet (σ 2 , a, Λ), where the Lévy measure Λ describes the intensity of the Poisson point process of births and jumps. We establish a version of Biggins' theorem [Big77] in this framework, that is we provide necessary and sufficient conditions in terms of the characteristic triplet (σ 2 , a, Λ) for additive martingales of branching Lévy processes to have a non-degenerate limit. The proof is adapted from Lyons [Lyo97].