AbstractIn this paper, we present a nonlinear strong positivity‐preserving finite volume (FV) scheme on tetrahedral meshes for nonstationary convection–diffusion equations with general right‐hand term, whose exact solution is assumed to be non‐negative, while the right‐hand term is allowed to be negative. A nonlinearization technique, which can be regarded as a correction of the linear scheme, is used to the discretization of both the diffusion and convection terms. Moreover, we impose nonlinear correction for the right‐hand term if it is a sink. The resulting scheme is cell‐centered and locally conservative, and has a fixed stencil. And in the construction of the scheme, it is unnecessary to assume that auxiliary unknowns are non‐negative. Besides, the existence of a solution and the strong positivity‐preserving property for the nonlinear system are proved. Finally, the numerical examples are presented to show the positivity of the new scheme and the second‐order convergence rate for the solution.