This study focuses on estimating O-D (origin-destination) trip demand from link traffic flows. Equality relationship among link traffic flow, path flow, and O-D trip matrices are used to establish a linear equation system. Solution characteristics are analyzed based on the relationship between the rank of the link/path incidence matrix and column variables. And under the solution framework of conditional inverse matrices, a column exchange method and a path flow proportion method have been developed. Network testing results verify that the proposed methods yield good results.