A sampling frequency conversion apparatus which easily controls the phase difference (time difference) between the input data and the output data in converting the sampling frequency, includes a storage device 13 for continuously writing the input data or the data obtained by over-sampling the input data and for continuously reading out the data written maintaining a predetermined address difference relative to the writable address, and an interpolation processing unit 14 for interpolating the data read-out from the storage device 13 to obtain data of which the sampling frequency is converted. In converting the sampling frequency, an address difference between a writable address and a readable address in the storage device 13 is optimized, the address difference being optimized without limitation for a predetermined period of time from the start of supplying the input data and, then, being optimized by imposing a predetermined limitation after the passage of the predetermined period of time.