Delay tomography has so far burdened source and receiver measurement nodes in a network with two requirements: 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 based on compressed sensing. The proposed scheme selects a path between source and receiver measurement nodes as the reference path, which results in a loss of equation in a conventional delay tomography problem. By utilizing compressed sensing, however, the proposed scheme becomes robust to the loss. Simulation experiments confirm that the proposed scheme works comparable to a conventional delay tomography scheme in a network with no clock synchronization between source and receiver measurement nodes.