In a parallel computer including L=n.sub.1 .times.n.sub.2 .times. - - - .times.n.sub.N processor element or external devices (hereafter represented by processor elements), an interconnection network of processor elements using L.times.(1/n.sub.1 +1/n.sub.2 + - - - +1/n.sub.N) crossbar switches in total comprises N dimensional lattice coordinates (i.sub.1, i.sub.2, - - - , i.sub.N), 0.ltoreq.i.sub.1 .ltoreq.n.sub.1 -1, 0.ltoreq.i.sub.2 .ltoreq.n.sub.2 -1; - - - , 0.ltoreq.i.sub.N ; and .ltoreq.n.sub.N -1 given to each processor element as the processor element number, crossbar switches for decoding a dimensional field in a processor element number having specific position and length depending upon the number of lattice points of a particular dimension and for performing the switching operation with regard to the dimension, interconnection of n.sub.k processor elements having processor element numbers, which are different only in the k-th dimensional coordinate for arbitrary k, i.e., having processor element numbers ##EQU1## by using one of the crossbar switches, each of the crossbar switches having n.sub.k inputs and n.sub.k outputs, and the interconnection performed with respect to all (L/n.sub.k sets) of coordinates (i.sub.1, i.sub.2, - - - , i.sub.k-1, i.sub.k+1, - - - , i.sub.N) of N-1 dimensional subspace excluding the k-th dimension, the interconnection being further performed for all values of k (1.ltoreq.k.ltoreq.N).