The normal grain growth behaviors at 750, 800 and 900°C in block and sheet samples of CuAlMn shape memory alloy with the bcc single-phase structure were investigated. The grain growth exponents, n, evaluated in the two-and three-dimensional grain growths were found to be larger than those in most other metals and were located between 10 and 18. Furthermore, the two-dimensional growth in thin sheet samples was much slower than the three-dimensional growth in block samples due to the grooves formed along grain boundaries on the specimen surface, these grooves constituting a hindrance to the movement.