In this article, we propose a new sequence of α-Bernstein-Kantorovich type operators based on a parameter ζ, and to study approximation behavior of our operators, we establish local and global approximation theorems. Also, we introduce bivariate α-Bernstein-Kantorovich operators and estimate the Voronovskaya type asymptotic theorem and the order of approximation using Peetre’s (Formula presented.) -functional. Lastly, using Maple software, we show the convergence of our newly defined operators to a certain function by graph.