To understand the characteristics of the anisoplanatic error resulting from different return-light experiences between the sodium beacon with a greater angular offset and the science object through atmospheric turbulence, the angular anisoplanatism for sodium beacon is investigated experimentally based on the technique of synchronized range gating. The return-light spot arrays through turbulent atmosphere from the natural star and the sodium beacon with 50 rad angular offsets are synchronously collected by using a single Hartmann wavefront sensor, consequently the synchronous turbulence-induced wavefront distortion sequences are recovered for the on-axis natural star and the off-axis sodium beacon. According to the experimental data, the temporal correlations of the wavefront distributions and decomposed Zernike modes between the on-axis natural star and the off-axis sodium beacon are discussed. By comparing the off-axis sodium beacon with the on-axis natural star, we analyse the statistics of the acquired angular anisoplanatism error and its associated Zernike-modal variances for the off-axis sodium beacon, and derive the Zernike-modal relative anisoplanatic errors as well. Furthermore, the influence of the acquired angular anisoplanatism error on the quality of imaging point spread function (PSF) is studied. The experimental results show that the existence of 50 rad angular deviation between the sodium beacon and the natural star causes that there are a certain correlation between just low-order Zernike modes of these two types of wavefronts (e.g. from the 3rd order to the 9th order), but the correlations between other high-order Zernike modes of these two types of wavefronts are severely degenerated and even these modes are de-correlated, resulting from the improper turbulence probing with off-axis sodium beacon off the ray path from the natural star to the telescope aperture. The angular anisoplanatism error has a great influence on the quality of imaging PSF, which leads to a degradation of Strehl ratio of 0.31-0.22 and beam quality factor of 2.70-3.35. Therefore, the influence may not to be ignored. At the end of this paper, according to the derived experimental turbulence coherence length and the generalized Hufnagel-Valley model, we calculate the theoretical anisoplanatic phase variance for the sodium beacon with 50 rad angular offsets, which is in good accordance with the measured anisoplanatic phase variance. This investigation is useful in promoting our knowledge of sodium beacon angular anisoplanatism effect on turbulence probing.