We model simultaneous or quasi-simultaneous multi-band spectral energy distributions (SEDs) for a sample of 25 blazars that have radio core-shift measurements, where a one-zone leptonic model and Markov chain Monte Carlo technique are adopted. In the SED fitting for 23 low-synchrotron-peaked (LSP) blazars, the seed photons from the broad-line (BLR) and molecular torus are considered respectively in the external Compton process. We find that the SED fitting with the seed photons from the torus are better than those utilizing BLR photons, which suggest that the gamma-ray emitting region may be located outside the BLR. Assuming the magnetic field strength in the gamma-ray emitting region as constrained from the SED fitting follows the magnetic field distribution as derived from the radio core-shift measurements (i.e., B(R) similar or equal to B-1 pc(R/1pc)(-1), where R is the distance from the central engine and B-1 pc is the magnetic field strength at 1 pc), we further calculate the location of the gamma-ray emitting region, R-gamma, for these blazars. We find that R-gamma similar to 2 x 10(4)Rs similar or equal to 10 R-BLR (R-S is the Schwarzschild radius and R-BLR is the BLR size), where R-BLR is estimated from the broad-line luminosities using the empirical correlations obtained using the reverberation mapping methods.