Spectral characteristics of normal female breast samples in the 350-850 nm wavelength range were measured using a UV/Vis/NIR spectrophotometer system with integrating sphere attachment for measuring the diffuse reflectance and transmittance. The optical properties of normal breast tissue in vitro were obtained by the inverse adding doubling method. And then the optical penetration depths in this spectral range were analyzed based on the principle of tissue optics. The results show that the reduced scattering coefficient of normal female breast tissue is significantly higher than the absorption coefficient in the 350-850 nm wavelength range. The reduced scattering coefficient decreases with the wavelength increment. It reaches maximum at shorter wavelengths with a decrease at longer wavelengths and ranges from 9.731 mm(-1) at 350 nm to 1.476 mm(-1) at 850 nm. The absorption coefficient of normal breast tissue is about from 0.798 mm(-1) at 350 nm to 0.102 mm(-1) at 850 nm. The maximal and minimal values are at 350 nm and 850 nm respectively. An absorption peak for the normal breast tissue is at 410 nm of wavelength with the value of 0.506 mm(-1), which belongs to hemoglobin. The absorption coefficient remains relatively constant when the wavelength is longer than 600 nm. The optical penetration depth increases with the wavelength increment and ranges about from 0.199 mm at 350 nm to 1.439 mm at 850 nm. Deep penetration depth noted in normal breast samples, especially at longer wavelengths, reflects the weak absorption and reduced scattering at these wavelengths. The calculated optical parameters of normal breast samples by the inverse adding doubling method agree well with the Monte Carlo simulations. This study may be useful for breast optical biopsy or the optical diagnosis of breast diseases.