A fast reservation protocol type ATM switching method and ATM switching equipment which are capable to suppress deterioration in transmission efficiency by reducing a cell discarding rate even in case of transmitting a huge ATM cell burst is provided. A buffer monitoring circuit monitors the number of idle slots in a buffer of an ATM switching equipment. A resource management (RM) cell processing circuit compares the number of idle slots with the total number of cells consisting an ATM cell burst contained in an RM cell locating at the top of the ATM cell burst stream when receiving the ATM cell burst from an ATM subscriber equipment. If the number of idle slots is not available for storing all cells in the ATM cell burst, the RM cell processing circuit instructs a gate circuit to pass same number of cells as idle slots available in the buffer and discard the rest of cells, and transmits a RM cell, containing information of number of cells to be retransmitted, to the ATM subscriber equipment for requesting retransmission.