This paper presents the evolution of the clustering of the main population of galaxies from z=2.1 to z=0.2, from the first epoch VIMOS VLT Deep Survey (VVDS), a magnitude limited sample with 17.5<=I_{AB}<=24. We have computed the correlation functions xi(r_p,pi) and w_p(r_p), and the correlation length r_0(z), for the VVDS-02h and VVDS-CDFS fields, for a total of 7155 galaxies in a 0.61deg^2 area. We find that the correlation length in this sample stays roughly constant from z=0.5 to z=1.1, with r_0(z)=2.5-2.8 h^{-1} Mpc (comoving), for galaxies comparable in luminosity to the local 2dFGRS and SDSS samples, indicating that the amplitude of the correlation function was ~2.5x lower at z~1 than observed locally. The correlation length in our lowest redshift bin z=[0.2,0.5] is r_0=2.4 h^{-1} Mpc, lower than for any other population at the same redshift, indicating the low clustering of very low luminosity galaxies, 1.5 magnitudes fainter than in the 2dFGRS or SDSS. The correlation length is increasing to r_0~3.0 h^{-1} Mpc at higher redshifts z=[1.3,2.1], as we are observing increasingly brighter galaxies, comparable to galaxies with MB_AB=-20.5 locally. We compare our measurement to the DEEP2 measurements in the range z=[0.7,1.35] citep{coil} on the population selected applying the same magnitude and color selection criteria as in their survey, and find comparable results. The slowly varying clustering of VVDS galaxies as redshift increases is markedly different from the predicted evolution of the clustering of dark matter, indicating that bright galaxies are already tracing the large scale structures emerging from the dark matter distribution 9-10 billion years ago, a supporting evidence for a strong evolution of the galaxy vs. dark matter bias.
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