Adjoint differentiation method is used in reconstruction algorithm for optical tomography by Alexander D. Klose, but the algorithm of getting derivatives with respect to optical parameters is mistakenly proposed by him, and it can only implement the computation of derivative with respect to optical parameters on the boundary, those derivatives with respect to the internal parameters cannot be obtained there. This will lead to the failure of the reconstruction. Based on the adjoint differentiation method, an improved algorithm with a tree structure is proposed for the computation of derivatives, and a specific method about the derivative with respect to internal optical parameters is put forward. In order to decrease the computation complexity, an approximate strategy about gradient computation is adopted in the experiment. Experimental results show that this kind of algorithm can implement the computation of derivatives with respect to internal optical parameters effectively. The approximate algorithm can make the computation less complex, improve the speed of computation and get good quality of reconstruction at the same time.