The parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. On the other hand, due to the advances in many application areas such as motion picture processing, computer animation, virtual reality systems, and so forth, it has become increasingly apparent that the study of four-dimensional patterns is of crucial importance. Therefore, we think that the study of four-dimensional automata as a computational model of four-dimensional pattern processing is also meaningful. In this article, we propose a four-dimensional parallel Turing machine (4-PTM), and investigate some of its properties based on hardware complexity.