A technique based on a successive approximation method is proposed to solve direct and inverse problems of radiative exchange among surfaces. With the present technique, the radiative exchange can be formulated by an expression in terms of some integrals and the surface reflectivity. The integrals are independent of the reflectivity and can be obtained by only one calculating procedure, provided that the geometry is fixed. The Monte Carlo method and the quadrature method are applied to perform the integration. Thus, after obtaining the integrals, the direct solutions for the values of the reflectivity of some concern to us can be readily obtained by substituting those values into the expression. Moreover, employing the present technique, we can solve an inverse problem estimating the surface reflectivity without solving the associated direct problem repetitively. Results of the three examples considered show that both of the direct and inverted results are in good agreement with the benchmark solutions.