  Supernova remnant RX J1713.7-3946 (also named as G347.3-0.5) has exhibited
largest surface brightness, detailed spectral and shell-type morphology, it is
one of the brightest TeV sources. The recent H.E.S.S. observation of RX
J1713.7-3946 revealed \textbf{a} broken power-law spectrum of GeV-TeV gamma-ray
spectrum and more extended gamma-ray spatial radial profile than that in the
X-ray band. Based on the diffusion shock acceleration model, we solve
spherically symmetric hydrodynamic equations and transport equations of
particles, and investigate multi-band non-thermal emission of RX J1713.7-3946
and radial profiles of its surface brightness for two selected zones in the
leptonic scenario for the $\gamma$-ray emission. We found (1) the diffusion
coefficient has a weak energy-dependent, and the Kolmogorov type is favored;
(2) the magnetic field strength could vary linearly or nonlinearly with radius
for different surrounding environments because of possible turbulence in shock
downstream region, and a compressional amplification is likely to exist at the
shock front; (3) the non-thermal photons from radio to X-ray bands are
dominated by synchrotron emission from relativistic electrons, if the GeV-TeV
gamma-rays are produced by inverse Compton scattering from these electrons
interacting with the background photons, then the X-ray and gamma-ray radial
profiles can be reproduced except for the more extended $\gamma$-ray emission.
