The absorption coefficient mu(a), scattering coefficient mu(s), and anisotropy factor g of diluted and undiluted human blood (hematocrit 0.84 and 42.1%) are determined under flow conditions in the wavelength range 250 to 1100 nm, covering the absorption bands of hemoglobin. These values are obtained by high precision integrating sphere measurements in combination with an optimized inverse Monte Carlo simulation (IMCS). With a new algorithm, appropriate effective phase functions could be evaluated for both blood concentrations using the IMCS. The best results are obtained using the Reynolds-McCormick phase function with the variation factor alpha = 1.2 for hematocrit 0.84%, and alpha = 1.7 for hematocrit 42.1%. The obtained data are compared with the parameters given by the Mie theory. The use of IMCS in combination with selected appropriate effective phase functions make it possible to take into account the nonspherical shape of erythrocytes, the phenomenon of coupled absorption and scattering, and multiple scattering and interference phenomena. It is therefore possible for the first time to obtain reasonable results for the optical behavior of human blood, even at high hematocrit and in high hemoglobin absorption areas. Moreover, the limitations of the Mie theory describing the optical properties of blood can be shown.