The current paper deals with the parametric modification of Bernstein operators which preserve constant and Korovkin's other test functions in limit case. The uniform convergence of the newly constructed operators is studied. Also, the rate of convergence is investigated by means of the modulus of continuity, by using functions which belong to Lipschitz class and by the help of Peetre's-K functionals. Finally, some numerical examples are given to illustrate the effectiveness of the newly defined operators for computing the approximation of function.