This paper proposes a multifunction radar that can not only measure sea currents but also perform sea-surface imaging. The fundamental aspect of the proposed radar comprises transmitting time-shifted up-and-down continuous wave linear frequency modulated signals that allow for the offset of two one-dimensional range images of the sea surface that respectively correspond to the upward linear frequency modulated (LFM) signal and the downward LFM signal. Owing to the Doppler frequency shift from the sea surface, a range offset, which is proportional to the radial velocity of the sea surface, occurs between the upward and downward LFM signals. By using the least-squares linear fitting method in the transformed domain, the range offset can be measured and the current velocity can be retrieved. Finally, we verify the accuracy of current measurement with simulation results.