The even-order dispersion cancellation effect based on the frequency anti-correlated photon pairs has attracted much attention in the research of quantum dispersion cancellation in two-photon systems. In this letter, we demonstrate a four-photon quantum interferometry in which we can not only observe the even-order dispersion cancellation effect but also the odd-order cancellation. Importantly, the four-photon scheme can get a much better resolution than the two-photon case and help us get a better understanding of the -interference phenomenon in a four-photon interferometry.