Optically levitated micro- and nano-particle system is an important platform for the study of many-body physics. However, the previous studies are mainly implemented in the liquid. Recently, due to the obvious advantages, the technique of optical levitation in a vacuum has attracted much attention. In this paper, we experimentally trap two nanoparticles using two individual strongly focused lasers in a vacuum and study the light-induced dipole-dipole interaction of the nanoparticles due to the scattering. In the experiment, a laser beam is directly divided into parts to individually trap two silica nanoparticles. The system is analogous to a Mach Zehnder interferometer (MZI), in which the two nanoparticles are sensitive to the interference intensity of the light fields and therefore can be regarded as reflective mirrors. The constructive or destructive interference of the light fields at the nanoparticles' positions directly determines the strength of the dipole-dipole interaction. This system reduces the noise caused by the phase flicker and improves the trapping stability compared to using a spatial light modulator. The light-induced dipole-dipole interaction is measured by adjusting the relative frequencies of the center-of-mass (CoM) motions (or torsional vibrations) of two nanoparticles near the frequency degeneracy point under different linear polarization conditions. The interaction of the torsional vibrations is not observed in this experiment, which indicates that the dipole scattering almost can't influence this motion mode. While a strong coupling between the CoM motions occurs when the polarizations of the trapping beams are perpendicular to the line between the two particles. The measured coupling strength is 1.6 kHz. This work is helpful for further studies of the non-reciprocal interaction between two nanoparticles via adjusting the distance between the nanoparticles and the phase difference of trapping beams, the collective motion of light-induced dipole-dipole interaction of nanoparticles, collaborative cooling and manipulation of multi-particle systems at the single-particle level. It provides a new technical route for studying the multi-particle system.