We have investigated the microstructural properties of a weakly charged polyelectrolyte modeled with both Hookean spring and Debye-Huckel potential, by employing a novel hybrid scheme of molecular dynamics (MD) and Monte Carlo (MC) simulations. Although the off-lattice pivot step facilitates the earlier computations stage, it gives rise to oscillations and hinders the stable equilibrium state. In order to overcome this problem, we adopt the MC off-lattice pivot step in early stage only, and then switch the computation to a pure MD step. The result shows that the computational speed-up compared to the previous method is entirely above 10 to 50, without loss of the accuracy. We examined the conformations of polyelectrolyte in solvents in terms of the end-to-end distance, radius of gyration, and structure factor with variations of the screening effects of solvent and the monomer charges. The emphasis can favorably be given on the elongation behavior of a polyelectrolyte chain, with observing the simultaneous snapshots.