Context. With the aid of stellar abundance analysis, it is possible to study the galactic formation and evolution. Magnesium is an important element to trace the alpha-element evolution in our Galaxy. For chemical abundance analysis, such as magnesium abundance, accurate and complete atomic data are essential. Inaccurate atomic data lead to uncertain abundances and prevent discrimination between different evolution models. Aims. We study the spectrum of neutral magnesium from laboratory measurements and theoretical calculations. Our aim is to improve the oscillator strengths ( f -values) of Mg I lines and to create a complete set of accurate atomic data, particularly for the near-IR region. Methods. We derived oscillator strengths by combining the experimental branching fractions with radiative lifetimes reported in the literature and computed in this work. A hollow cathode discharge lamp was used to produce free atoms in the plasma and a Fourier transform spectrometer recorded the intensity-calibrated high-resolution spectra. In addition, we performed theoretical calculations using the multiconfiguration Hartree-Fock program ATSP2K. Results. This project provides a set of experimental and theoretical oscillator strengths. We derived 34 experimental oscillator strengths. Except from the Mg I optical triplet lines (3p 3^P^o_0,1,2 - 4s 3^S_1), these oscillator strengths are measured for the first time. The theoretical oscillator strengths are in very good agreement with the experimental data and complement the missing transitions of the experimental data up to n = 7 from even and odd parity terms. We present an evaluated set of oscillator strengths, gf, with uncertainties as small as 5%. The new values of the Mg I optical triplet line (3p 3^P^o_0,1,2 - 4s 3^S_1) oscillator strength values are ~0.08 dex larger than the previous measurements.