With the extension of the energy equation of turbid density flow to the whole water depth of sediment-laden flow, the formula of equilibrium sediment concentration under the condition of steady state is obtained. On this basis, with the theory of minimum rate of flow energy dissipation, a formula of sediment carrying capacity is derived. In addition, the coefficient of the formula is proportional to the coefficient of hydraulic resistance. In different flow regions, including laminar region, turbulent smooth region, turbulent transition region, turbulent rough region, the coefficient of hydraulic resistance changes with the exponential change of the Reynolds number. In different turbulent flow, the general formula can be evolved into the sediment carrying capacity formula forms of Han Qiwei, Dou Guoren, Liu Jiaju and Zhang Ruijin. The relationship between this formula and other sediment carrying capacity formula which have been done is revealed. And this formula can be used as a general formula is confirmed. The formula is compared with the Liu Jiaju's formula and the Zhang Ruijin's which have been used for many years by the measured data. It is shown that this formula has certain advantages.