With simple mathematic theory, the approximate relation between the statistic parameter of the comput- ing result's error of the analytical solution of one dimension stream water quality equation and that of original data error has been established in this paper, and correspondingly the conditional numbers which can be used to describe the performance of computing problem have been derived. On the base of these, the performance of the direct and inverse computing problems being"ill-conditioned" or"well-conditioned" has been analysized.