We have demonstrated the highly nondegenerate four-wave mixing among sub-picosecond optical pulses in a 1.3 micrometers multiple-quantum well semiconductor optical amplifier (SOA). We could directly measure the four-wave mixing signal in the output spectrum by current pulse pumping of the device. We achieved a high conversion efficiency of over 10% at a frequency conversion range of less than 1 THz. The limitation of conversion efficiency due to the gain saturation of the SOA was effectively overcome by using the short optical pulses. Preliminary results of optical sampling with picosecond time resolution are also described.