In the paper, we prove the discrete universality theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the derivatives of L-functions of elliptic curves. We consider an approximation of analytic functions by translations L‘E (s + imh), where h > 0 is a fixed number, the translations of the imaginary part of the complex variable take values from some arithmetical progression. We suppose that the number h > 0 is choosen so that exp{2πk/h} is an irrational number for all k ∈ Z \{0}. The proof of discrete universality of the derivative L-functions of elliptic curves is based on a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions.