Measuring velocity spectra in turbulent flows requires methods providing a high temporal resolution and a low measurement uncertainty. Hot-wire anemometry is often used, but it is intrusive. Laser Doppler anemometry is non-intrusive, but due to the statistical arrival of individual tracers provides no constant measurement rate. We therefore propose the use of Doppler global velocimetry (DGV), which is a contactless method allowing temporally equidistant measurements of continuous signals. Additionally, 2d measurements are possible instead of single point measurements. The commonly applied slow cameras are substituted by a fibre coupled detector array consisting of 25 avalanche photo diodes, which increases temporal resolution up to 10 μs. Contrarily to conventional DGV, a sinusoidal laser frequency modulation enables omitting the reference detector array. A correction of beam splitting and image misalignment errors is thus not necessary, but disturbances due to temporal fluctuations of the scattered light can occur and have to be reduced by increasing the modulation frequency. We validate the proposed system capability of synchronously measuring velocity spectra at multiple points in turbulent flows by presenting experimental results. The acquired velocity spectra in a wind tunnel experiment show good agreement with hot-wire comparison measurements within 0.1 m/s. An uncertainty analysis is given, which allows the achievable measurement uncertainty to be estimated as a function of the desired temporal resolution. An uncertainty down to 0.2 m/s can, for example, be achieved assuming a desired temporal resolution of 1 ms. These promising results open new perspectives for turbulence and correlation studies in flows such as to investigate the turbulence characteristics behind a truncated cylinder attached to a plate or the inlet of an aircraft turbine for flow characterisation in industry.