The spectra and predissociation dynamics of the Rydberg states 4pσB″1∑u+(υ'=2) and 4pπD'1Πu±(υ'=1) of the D2 molecule have been studied by a combination of XUV laser pump, UV laser probe, and velocity map imaging methods. The D(2l) fragment yield spectrum and the D2 excitation spectrum have been measured. Although the predissociation rates were found to be small and comparable to the radiative decay rates, the D(2l) fragments were observed for all the Rydberg states. The measured D(2l) fragment angular distributions are in good agreement with a reported model that has an analytical formula for anisotropy parameters. The results demonstrated that the 4pσB″1∑u+ and 4pπD'1Π u+ states dissociate via direct and indirect coupling with an 1∑u+ state, respectively. For predissociation of the 4pσB″1∑u+ state, the experimental data showed that D(1s) + D(2s) is the main channel, supporting previous theoretical predictions that the predissociation occurs by coupling to the vibrational continuum of the 3pσB'1∑u+ state.