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We present the semi-Lagrangian approximation of transfer operator for three-dimensional convection-diffusion problem with corresponding initial and boundary conditions. This problem describes, for instance, a transfer of a substance with diffusion. To construct numerical method, we decompose operator of this equation into two parts. The first one is the transfer operator. The second part is the elliptic diffusion terms. To approximate the first part, we use conservative semi-Lagrangian approximation connecting two integrals of solution at neighboring time levels. To compute integral at the previous time level, we approximate integral domain by 48 tetrahedrons and interpolate solution by trilinear functions. The second part is approximated by conventional finite differences. Finally, we combine approximations of two parts to get a system of linear equations at each time level. Matrix of this system at each time level is the symmetric M-matrix. The proposed approximation has the first-order convergence that is confirmed by computational experiments. [ABSTRACT FROM AUTHOR]