In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments. © 2018, University of Nis. All rights reserved.