A biological sample measurement apparatus includes a measurement component for detecting a blood glucose level, a transmitter for sending the detected blood glucose level to a portable terminal, a receiver for receiving an acknowledge signal and a portable terminal ID sent from the portable terminal, a storage component for associating the communication frequency at the point of successful communication with the received portable terminal ID and storing it as communication success history along with successful information from the past, and a communication frequency selector for selecting a communication frequency on the basis of this communication success history.