1. An SIMD parallel computer system that performs parallel processing with two or more processing elements coupled in a ring form for different data values under a single instruction stream, wherein each of the processing elements comprises: a data storage module that stores data processed by each of the processing elements; a number-of-data-sets storage device that stores number of data sets of the data; and a data storage device that stores a part of the data stored in the data storage module, the system further comprising a control processor that compares first number-of-data-sets of the data stored in the number-of-data-sets storage device of one processing element out of the two or more processing elements coupled in the ring form with second number-of-data-sets of the data stored in the number-of-data-sets storage device of the own processing element, and issues, to each of the processing elements, a data distribution leveling instruction that designates an action for updating contents of the data stored in the data storage module, the number-of-data-sets storage device, and the data storage device of the own processing element according to a rule that is determined based on a comparison result of the own processing element, and a comparison result of the other processing elements and an action for moving the data stored in the one processing element to the own processing element.