We introduce generalized Bernstein--Kantorovich type operators with two shifted nodes and study their approximation properties. First, we calculate some estimates for these operators. Further, we discuss convergence theorems and order of approximation in terms of Korovkin theorem and first order modulus of smoothness respectively. Next, we study pointwise approximation results in terms of Peetre's K-functional, second order modulus of smoothness, Lipschitz type space and $r^{th}$ order Lipschitz type maximal function. Lastly, weighted approximation results and statistical approximation theorems are proved.