The 3Λu state of Na2 is excited by using optical-optical double resonance spectroscopy. The predissociative rates and collisional transfer rates of 3Λu state are experimentally measured. The cell temperature varies between 553 K and 703 K. A continuous-wave (CW) all-solid-state green laser (532 nm) is used to pump Na2 from ground state 13Σ+u to the 13Σ+g. Then an optical parameter oscillator (OPO) laser is used to excite high-lying 3Λu state. From time-resolved fluorescence for the 3Λu→13Σ+g transition at different Na densities,the effective lifetimes of the Na2(3Λu) state are yielded. Based on the Stern-Volmer equation,the sum of the radiative and predissociative rates is obtained with (4.8±1.2)×107 s-1,and the total cross section for deactivation of the Na2(3Λu) by means of collisions with Na is (2.7±0.5)×10-14 cm2. With different Na densities,the time-integrated intensities of 3Λu→13Σ+g,5S→3P and 3D→3P radiative transition are measured. The intensity ratios versus the Na densities can be fitted by the straight lines. From the slopes and the intercepts,we obtain predissociative rate of (8.0±2.4)×106 s-1 from Na2(3Λu) to Na(3D),and the cross sections of (6.2±1.9)×10-15 cm2 and (1.1±0.3)×10-15 cm2 for collisional energy transfer from Na2(3Λu) to Na(5S) and from Na2(3Λu) to Na(3D),respectively.