Delay tomography has so far burdened source and receiver measurement nodes in a network with two requirements such as path establishment and clock synchronization between them. In this letter, we focus on the clock synchronization problem in delay tomography and propose a synchronization-free delay tomography scheme. The proposed scheme selects a path between source and receiver measurement nodes as a reference path, which results in a loss of equation in a conventional delay tomography problem. However, by utilizing compressed sensing, the proposed scheme becomes robust to the loss. Simulation experiments confirm that the proposed scheme works comparable to a conventional delay tomography scheme in networks with no clock synchronization between source and receiver measurement nodes.