We propose a two-dimensional scanning laser Doppler velocimeter (LDV) that does not require any moving mechanisms in its probe. In the proposed LDV, the measurement position can be scanned in two dimensions on a cross-sectional plane perpendicular to the direction of flow. The combination of the change in wavelength and change in port of the fiber array input to the probe is utilized for the scan. The experimental results using a sensor probe setup indicate that the measurement position can be scanned in two dimensions using the proposed method. The scanning range was estimated to be 39.7 mm in the axial direction over the wavelength range of 1536-1554 nm and 26.1 mm in the transverse direction for the use of 22 ports of the fiber array.