<p>The hydroxyl radical (OH) determines the atmospheric self-cleaning capability and is one of the significant oxidants in atmospheric photochemistry reactions. The global OH has been monitored by satellites with the traditional limb mode in the past decades. This observed mode can achieve high-resolution vertical OH data, but cannot obtain the enough horizontal OH data for inverting high-precision OH concentrations because OH has the high reactivity that makes its concentrations extremely low and distributions complicated. The Double Spatial Heterodyne Spectrometers (DSHS) is designed in order to achieve more high-resolution and detailed OH data. This sensor can measure the OH by the three-dimensional limb mode to obtain the comprehensive OH data in the atmosphere. We propose a new tomographic retrieval algorithm here based on the simulated observation data due to the DSHS will work officially on the orbit in the future. We build up an accurate forward model that the main part of it is the SCIATRAN radiative transfer model which is modified according to the radiation transmission theory. We also construct the tomographic retrieval algorithm that the core is a look up table method. A tomographic observed database is built up through the atmospheric model, the spatial information (position of the target area and satellite position), the date parameters, the observation geometries, OH concentrations and simulated observation data. The OH concentrations can be found directly from it. If there are no corresponding query conditions in the tomographic observed database, the cubic spline interpolation is used to obtain the OH concentrations. The tomographic retrieval algorithm can obtain the more accurate OH concentrations even in the lower atmosphere where the OH data is not well and avoids the initial guess values for solving the iteration problems. Our research not only provides a scientific theory support for the construction of DSHS, but also gives a new retrieval algorithm idea for other radicals.</p>