The finite-volume method is applied to the second-order radiative transfer equation, proposed by Zhao and Liu, to study its accuracy and solution cost for two simple two-dimensional problems. The second-order equation leads to results that are accurate and bounded, but the iterative solution of the equations is expensive, especially for weakly participating media. The high cost is due mainly to the elliptic character of the second-order equation and the lack of diagonal dominance of the algebraic equations.