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The paper deals with numerical solving nonlinear integro-parabolic problems based on an alternating direction implicit (ADI) scheme. A monotone iterative ADI method is constructed. An analysis of convergence of the monotone iterative ADI method is given. References I. Boglaev, Monotone alternating direction implicit scheme for nonlinear parabolic problems. BIT Numerical Mathematics, 55, 2015, 647-676. doi:10.1007/s10543-014-0529-6 J. Douglas, H. H. Rachford, On the numerical solution of heat condition problems in two and three variables. Trans. Amer. Math. Soc., 82, 1956, 421–439. G. I. Marchuk, Splitting and alternating direction methods, Handbook of Numerical Analysis, 1, 197–462. (Eds P. Ciarlet, J. Lions). North-Holland, Amsterdam, 1990. R. McLachlan, G. Quispel, Splittings methods. Acta Numer., 11, 2002, 341–434. doi:10.1017/S0962492902000053 C. V. Pao, Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, 1992. A. Samarskii, The Theory of Difference Schemes. Marcel Dekker, New York–Basel, 2001. I. H. Sloan, V. Thomee, Time distretization of an integro-differential equation of parabolic type. SIAM J. Numer. Anal., 23, 1986, 1052–1061. doi:10.1137/0723073 A. H. Stroud, Approximate Calculation of Multiple Integrals. Prentice–Hall, Englewood Cliffs, NJ, 1971.