Accelerated Molecular Dynamics (aMD) is a promising enhanced sampling method to explore the conformational space of biomolecules. However, the large statistical noise in reweighting limits its accuracy to recover the original free energy profile. In this work, we propose an Integrated accelerated Molecule Dynamics (IaMD) method by integrating a series of aMD subterms with different acceleration parameters to improve the sampling efficiency and maintain the reweighting accuracy simultaneously. We use Alanine Dipeptide and three fast-folded proteins (Chignolin, Trp-cage, and Villin Headpiece) as the test objects to compare our IaMD method with aMD systematically. These case studies indicate that the statistical noise of IaMD in reweighting for free energy profiles is much smaller than that of aMD at the same level of acceleration and simulation time. To achieve the same accuracy as IaMD, aMD requires 1-3 orders of magnitude longer simulation time, depending on the complexity of the simulated system and the level of acceleration. Our method also outperforms aMD in controlling systematic error caused by the disappearance of the low-energy conformations when high acceleration parameters are used in aMD simulations for fast-folded proteins. Furthermore, the performance comparison between IaMD and the Integrated Tempering Sampling (ITS) in the case of Alanine Dipeptide demonstrates that IaMD possesses a better ability to control the potential energy region of sampling.