Disclosed is an ATM switching apparatus capable of reducing a probability an IAM acceptance being rejected due to a difference in bandwidth acquiring algorithm. The ATM switching apparatus is constructed such that when receiving an IAR due to the difference in bandwidth calculation algorithm for the IAM indicating a use of a certain VPC, a calculated bandwidth value is set in an estimated free bandwidth value about the VPC within a bandwidth management table, a value given by Calculation Bandwidth Value/Free bandwidth Value is set in a ratio, and the VPC is selected by using not the free bandwidth value but the estimated free bandwidth value (=Free Bandwidth Value×Ratio) when transmitting the IAM. It is another contrivance that when the free bandwidth value changes, the estimated free bandwidth value is also changed to establish “Estimated Free Bandwidth Value=Free Bandwidth Value×Ratio” without changing the ratio.