Abstract This study is designed to develop an acceleration response spectrum that can be used in vibration serviceability assessment of civil engineering structures, such as floors and grandstands those are dynamically excited by individual bouncing. The spectrum is derived from numerical simulations and statistical analysis of acceleration responses of a single degree of freedom system with variable natural frequency and damping under a large number of experimentally measured individual bouncing loads. Its mathematical representation is fit for fast yet reliable application in design practice and is comprised of three equations that describe three distinct frequency regions observed in the actual data: the first resonant plateau (2–3.5 Hz), the second resonant plateau (4–7 Hz) and a descension region (7–15 Hz). Finally, this paper verifies the proposed response spectrum approach to predict structural vibration by direct comparison against numerical simulations and experimental results.