Using the optical-optical double resonance (OODR) technique, we have studied the collisional broadening of some 2^1Delta_g<--B^1Pi_u lines in Na2 molecules. A single line Ar+ laser is used to pump the sodium dimers from thermally populated ground state X^1Sigma+_g level to the intermediate B^1Pi_u state. Then, a single-mode diode laser is used to probe the doubly excited 2^1Delta_g state. The broadening rate coefficient is determined from the slope of the total linewidth versus Ne density curve. We obtain the average value k_(br)=(1.1+-0.5)*10^(-8) cm3/s. The collisional excitation transfer between rotational levels of the B^1Pi_u state (i.e., B^1Pi_u(2,83/84)<--B^1Pi_u(2,82)) is also investigated. The rates can be determined from the relative intensities of the main peak and satellite lines, combined with a rate equation model. The rates of 1.25*10^(6) and 1.07*10^(6) /s are obtained, respectively.