A parallel computer and all-to-all communications method. A plurality of processors are connected in an n-dimensional torus network, to provide an optimum communication method and apparatus for completing all-to-all communications within a shortest possible time. In the parallel computer having an n-dimensional rectangular parallelopiped torus network having a.sub.1 .times.a.sub.2 .times. . . . .times.a.sub.n processors, with the maximum value of a.sub.1, a.sub.2, . . . , a.sub.n defined as a.sub.max, it comprises a phase control unit having a phase control table for storing information according to which destination processors are determined for each of the predetermined transmission phases of a.sub.max P/4 (where P indicates the total number of processors) for a one-directional inter-processor connection channel, and of a.sub.max P/8 for a two-directional inter-processor connection channel, and a message transmission unit for transmitting a message to a destination processor listed in the phase control table during the phase in which the present processor is a source processor according to the predetermined phase order.