In this paper, a new method for interval solution of the $n^{th}$order linear ordinary differential equations (ODEs) with intervalinitial conditions is constructed. In this approach, by using theNeher's algorithm \cite{ref1}, first we obtain a guaranteedenclosure solution for an initial point value problem and thenbased on the Moore's idea \cite{ref2021,ref3}, we transform thissolution to arrive at an interval solution for the main problem.For the sake of clarity, we present an algorithm in terms of thelinear second order ODEs ($n=2$). Finally, some numerical examplesare presented to demonstrate the efficiency of the proposedalgorithm.