© Zagreb Paper JMI-15-59In this paper, we consider a new family of generalized Bernstein-Schurer-Stancu operators, depending on a non-negative real parameter α and study some approximation properties of these operators. We obtain a recurrence formula concerning calculation of moments by Schurer-Stancu operators. We prove a uniform approximation result using the well-known Korovkin theorem and obtain the rate of convergence in terms of modulus of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type results for these operators. Moreover, we give some numerical examples to illustrate approximation by the new operator.