We have investigated the growth shape of two-dimensional (2D) poly(ethylene terephthalate) spherulites using a transmission electron microscope technique in order to examine the role of a diffusion-controlled mechanism in the growth process. At the growth front of the 2D spherulites, we found a terrace-like morphology having a single crystal structure. The growth front of the terrace shows instabilities of periodic or groove patterns which can be explained by the diffusion-controlled theory for crystal growth.