In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs.