In this paper, we introduce a generalization of Szász–Mirakyan operators based on q-integers, that we call q-Szász–Mirakyan operators. Depending on the selection of q, these operators are more flexible than the classical Szász–Mirakyan operators while retaining their approximation properties. For these operators, we give a Voronovskaya-type theorem related to q-derivatives. Furthermore, we obtain convergence properties for functions belonging to particular subspaces of C[0,∞) and give some representation formulas of q-Szász–Mirakyan operators and their rth q-derivatives.