In chemical graph theory, Wiener index is a topological index of a molecule, defined as the sum of the lengths of the shortest paths between all pairs of vertices in the chemical graph representing the non-hydrogen atoms in the molecule. Calculation of Wiener index is usually done using distance matrix. For any matrix calculation smaller the matrix, better and fast are the computations. This paper aims to obtain the Wiener index of chemical trees by reducing the size of the distance matrix.