The authors give conditions on the ratios of dissection of a generalized Cantor set \(F\) (called Moran set) so that its algebraic sum \[ \underbrace{F+F+\ldots+F}_{n} \] has positive Lebesgue measure for sufficiently big \(n\). The theorem is an analogue of a theorem in [\textit{C. A. Cabrelli, K. E. Hare} and \textit{U. M. Molter}, ``Sums of Cantor sets'', Ergodic Theory Dyn. Syst. 17, 1299-1313 (1997; Zbl 0891.28001)] for a slightly more general definition of Cantor sets.