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In the present paper, Kantorovich type <inline-formula> <math display="inline"> <semantics> <mi>&#955;</mi> </semantics> </math> </inline-formula>-Bernstein operators via (<i>p</i>, <i>q</i>)-calculus are constructed, and the first and second moments and central moments of these operators are estimated in order to achieve our main results. An <i>A</i>-statistical convergence theorem and the rate of <i>A</i>-statistical convergence theorems are obtained according to some analysis methods and the definitions of <i>A</i>-statistical convergence, the rate of <i>A</i>-statistical convergence and modulus of smoothness.