The Ważewski method associated with the convergence of successive approximations is used in order to obtain existence and uniqueness results for the functional-integral equation of Volterra-Fredholm type of the form \[ \begin{multlined} x(t)=F \Biggl( t,x(t), \int_ 0^ t f_ 1(t,s,x(s))ds,\dots, \int_ 0^ t f_ n(t,s,x(s))ds,\\ \int_ 0^ T g_ 1(t,s,x(s))ds,\dots, \int_ 0^ T g_ n(t,s,x(s))ds \Biggr),\quad t\in[0,T].\end{multlined} \] It is assumed that the values of the functions involved belong to a Banach space. The reader is advised to be careful while reading this paper as there are some mistakes and misprints in the text.