We consider the reaction-diffusion system with delay {partial derivative u/partial derivative t = A (t, x)Delta u - Sigma(k)(i=1) gamma(i) (t, x)partial derivative(xi) u + f(t, u(t)), x is an element of Omega; B(u)vertical bar(partial derivative Omega) = 0. We show that this system with delay preserves positivity if and only if its diffusion matrix A and convection matrix gamma(i) are diagonal with non-negative elements and nonlinear delay term f satisfies the normal tangential condition.