It is shown, for the first time, that the Zitterbewegung of photons can appear near the Dirac point in a two-dimensional photonic crystal. The superiority of such a phenomenon for photons is that it can be found in different scaling structures with wide frequency regions. It can be observed by measuring the time dependence of the transmission coefficient through photonic crystal slabs. Thus, it is particularly suited for experimentally observing this effect. We have observed such a phenomenon by exact numerical simulations, confirming a long-standing theoretical prediction.