We consider a Lévy driven stochastic convolution, also called continuous time Lévydriven moving average model, X(t) = t 0 a(t − s)dZ(s) where Z is a Lévy martingale and the kernel a(.) a deterministic function square integrable on R +. Given N i.i.d. continuous time observations (Xi(t)) t∈[0,T ] on [0, T ], for i = 1,. .. , N distributed like (X(t)) t∈[0,T ] , we propose two types of nonparametric projection estimators of a 2 under dierent sets of assumptions. We bound the L 2-risk of the estimators and propose a data-driven procedure to select the dimension of the projection space.