A novel algebraic iterative algorithm based on deflection tomography is presented. This algorithm is derived from the essentials of deflection tomography with a linear expansion of the local basis functions. By use of this algorithm the tomographic problem is finally reduced to the solution of a set of linear equations. The algorithm is demonstrated by mapping a three-peak Gaussian simulative temperature field. Compared with reconstruction results obtained by other traditional deflection algorithms, its reconstruction results provide a significant improvement in reconstruction accuracy, especially in cases with noisy data added. In the density diagnosis of a hypersonic wind tunnel, this algorithm is adopted to reconstruct density distributions of an axial symmetry flow field. One cross section of the reconstruction results is selected to be compared with the inverse Abel transform algorithm. Results show that the novel algorithm can achieve an accuracy equivalent to the inverse Abel transform algorithm. However, the novel algorithm is more versatile because it is applicable to arbitrary kinds of distribution.