Measurement of the solar wind speed near the Sun is important for understanding the acceleration mechanism of the solar wind. In this Letter, we determine 2D solar wind speeds from 6 to 26 solar radii by applying Fourier motion filters to SOHO/LASCO C3 movies observed from 1999 to 2010. Our method successfully reproduces the original flow speeds in the artificially generated data as well as streamer blobs. We measure 2D solar wind speeds from one-day to one-year timescales and their variation in solar cycle 24. We find that the solar wind speeds at timescales longer than a month in the solar maximum period are relatively uniform in the azimuthal direction, while they are clearly bimodal in the minimum period, as expected from the Ulysses observations and interplanetary radio scintillation reconstruction. The bimodal structure appears at around 2006, becomes most distinctive in 2009, and abruptly disappears in 2010. The radial evolution of the solar wind speeds resembles the Parker's solar wind solution.