This study presents a case study on ground response analysis of one of the important cultural heritages in Hanoi, Vietnam. One-dimensional nonlinear and equivalent linear site response analyses which are commonly applied to solve the problem of seismic stress wave propagation are performed at the Ba Dinh square area. A measured in-situ shear wave velocity profile and corresponding geotechnical site investigation and laboratory test data are utilized to develop the site model for site-specific ground response analysis. A suite of earthquake records compatible with Vietnamese Design Code TCVN 9386: 2012 rock design spectrum is used as input ground motions at the bedrock. A few concerns associated with site-specific ground response evaluation are analyzed for both nonlinear and equivalent linear procedures, including shear strains, mobilized shear strength, and peak ground acceleration along with the depth. The results show that the mean maximum shear strains at any soil layer are less than 0.2% in the study area. A deamplification portion within the soil profile is observed at the layer interface with shear wave velocity reversal. The maximum peak ground acceleration (PGA) at the surface is about 0.2 g for equivalent linear analysis and 0.16 g for nonlinear analysis. The ground motions are amplified near the site natural period 0.72 s. The soil factors calculated in this study are 1.95 and 2.07 for nonlinear and equivalent linear analyses, respectively. These values are much different from the current value of 1.15 for site class C in TCVN 9386: 2012. A comparison of calculated response spectra and amplification factors with the local standard code of practice revealed significant discrepancies. It is demonstrated that the TCVN 9386: 2012 soil design spectrum is unable to capture the calculated site amplification in the study area.