The measurements of magnetic flux density ( Bz) needed in magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance current density imaging (MRCDI) techniques often utilize spin echo (SE)-based sequences for data acquisition. The low imaging speed of SE-based methods significantly hampers the clinical applications of MREIT and MRCDI. Here, we propose a new sequence for substantially accelerating the acquisition of Bz measurements. A skip-echo acquired turbo spin echo (SATE) imaging sequence based on the conventional turbo spin echo (TSE) technique was proposed by adding a skip-echo module in front of the TSE acquisition module. The skip-echo module consisted of a series of refocusing pulses without acquisition. In SATE, amplitude-modulated crusher gradients were used to remove the stimulated echo pathways, and the radiofrequency (RF) pulse shape was specially selected to preserve more signals. In efficiency evaluation experiments performed on a spherical gel phantom, we demonstrated that SATE had improved measurement efficiency compared to the conventional TSE sequence via skipping one echo before acquiring signals. The accuracy of the Bz measurements by SATE was validated against those by the multi-echo injection current nonlinear encoding (ME-ICNE) method, while SATE was able to accelerate the data acquisition up to 10-fold. Volumetric coverage of Bz maps obtained in the phantom, pork, and human calf illustrated that SATE can reliably measure volumetric Bz distributions within clinically acceptable time. The proposed SATE sequence provides a fast and effective approach for volumetric coverage of Bz measurements, greatly facilitating the clinical applications of MREIT and MRCDI techniques.