A coarse-grained modeling is based on the frnitely extendable nonlinear elastic (FENE) spring with long-range electrostatic and hydrodynamic interactions between pairs of beads, where both flexible and semiflexible chains are developed. We also consider steric and electrostatic interactions between the bead and the confining walls of different charge condition. Brownian dynamics simulations with the xanthan polyelectrolyte in bulk solutions and under confinement in a slit channel revealed an interesting crossover behavior from the 3D chain to a 2D one. For experimental verifications, single molecule visualization is performed on fluorescently labeled xanthan using an inverted epi-fluorescence microscope. Both the conformation and diffusivity of single xanthan molecules are characterized with variations of the chain confinement and solution environments. We discuss the scaling predictions to describe the source of the observed free-draining diffusion dynamics.