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We present spectral analysis of the Crab Nebula obtained with the {\it Chandra} X-ray observatory. The X-ray spectrum is characterized by a power-law whose index varies across the nebula. The variation can be discussed in terms of the particle injection from the pulsar in two different directions: the equatorial plane containing the torus and the symmetry axis along the jet. In the equatorial plane, spectra within the torus are the hardest, with photon index $\alpha \approx 1.9$, and are almost independent of the surface brightness. At the periphery of the torus, the spectrum gradually softens in the outer, lower surface brightness regions, up to $\alpha \approx 3.0$. This indicates that synchrotron losses become significant to X-ray emitting particles at the outer boundary of the torus. We discuss the nature of the torus, incorporating information from observations at other wavelengths. Spectral variations are also seen within the southern jet. The core of the jet is the hardest with $\alpha \approx$ 2.0, and the outer sheath surrounding the core becomes softer with $\alpha$ up to 2.5 at the outermost part. Based on the similarity between the spectra of the jet core and the torus, we suggest that the electron spectra of the particles injected from the pulsar are also similar in these two different directions. The brightness ratio between the near and far sides of the torus can be explained by Doppler boosting and relativistic aberration; however, the observed ratio cannot be derived from the standard weakly magnetized pulsar wind model. We also found a site where an optical filament comprised of supernova ejecta is absorbing the soft X-ray emission ($<$ 2 keV).