A common approach for spectrum determination of polyenergetic proton bunches from laser-ion acceleration experiments is based on the time-of-flight (TOF) method. However, spectra obtained using this method are typically given in relative units or are estimated based on some prior assumptions on the energy distribution of the accelerated ions. In this work, we present a new approach using the TOF method that allows for an absolute energy spectrum reconstruction from a current signal acquired with a sub-nanosecond fast and 10 μm thin silicon detector. The reconstruction is based on solving a linear least-squares problem, taking into account the response function of the detection system. The general principle of signal generation and spectrum reconstruction by setting up an appropriate system response matrix is presented. Proof-of-principle experiments at a 12 MV Tandem accelerator using different nanosecond-short (quasi-)monoenergetic and polyenergetic proton bunches at energies up to 20 MeV were successfully performed. Within the experimental uncertainties of 2.4% and 12.1% for energy and particle number, respectively, reconstructed energy distributions were found in excellent agreement with the spectra calculated using Monte Carlo simulations and measured by a magnetic spectrometer. This TOF method can hence be used for absolute online spectrometry of laser-accelerated particle bunches.