In this paper, a linear boundary value problem for the delay integro-differential equation is considered on a finite interval. By dividing the interval with a step equal to the delay and introducing additional parameters, the boundary value problem is reduced to a multipoint boundary value problem with parameters. The equivalence of the considered initial problem and the obtained multipoint problem is shown. A modified algorithm of the Dzhumabaev parameterization method for finding the solution of the multipoint boundary value problem is constructed. The conditions of existence and convergence of the proposed algorithm are established. The conditions of unique solvability of the boundary value problem for the delay integro-differential equation are obtained.