Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit. We describe the structure of the Lie algebra of derivations of the current Lie algebra gA=g⊗KA, denoted by Der(gA). Furthermore, we obtain the Levi decomposition of Der(gA). As a consequence of the last result, if hm is the Heisenberg Lie algebra of dimension 2m+1, we obtain a faithful representation of Der(hm,k) of the current truncated Heisenberg Lie algebra hm,k=hm⊗K[t]/(tk+1) for all positive integer k.