A portable terminal includes a GPS processing unit and RTC oscillator. In the GPS processing unit, a free-run RTC counter continuously counts real time clocks generated by the RTC oscillator even in the power saving mode, a time maintenance processing unit which includes a memory storing the count value of the free-run RTC counter and a notified GPS time upon a shift from a normal power mode to the power saving mode, calculates the duration of the power saving mode from the difference between the count value stored in the memory and the count value read from the free-run RTC counter upon return from the power saving mode to the normal power mode, and calculates the current GPS time by adding the calculated duration of the power saving mode to the stored GPS time upon a shift from the normal power mode to the power saving mode, and a position measurement processing unit performs position measurement by receiving a radio wave from the GPS satellite in the normal power saving mode, also notifies the time maintenance processing unit of the GPS time acquired when position measurement is performed, and performs position measurement by using the GPS time notified from the time maintenance processing unit upon a shift from the power saving mode to the normal power mode. A GPS keeping method is also disclosed.