The CMS collaboration has reported a 2.8σ excess in the search of the SU(2)_R gauge bosons decaying through right-handed neutrinos into the two electron plus two jets (eejj) final states. This can be explained if the SU(2)_R charged gauge bosons (W_R)^± have a mass of around 2 TeV and a right-handed neutrino with a mass of O(1) TeV mainly decays to electron. Indeed, recent results in several other experiments, especially that from the ATLAS diboson resonance search, also indicate signatures of such a 2 TeV gauge boson. However, a lack of the same-sign electron events in the CMS eejj search challenges the interpretation of the right-handed neutrino as a Majorana fermion. Taking this situation into account, in this paper, we consider a possibility of explaining the CMS eejj excess based on the SU(2)_L ⊗ SU(2)R ⊗ U(1)(B-L) gauge theory with pseudo-Dirac neutrinos. We find that both the CMS excess events and the ATLAS diboson anomaly can actually be explained in this framework without conflicting with the current experimental bounds. This setup in general allows sizable left-right mixing in both the charged gauge boson and neutrino sectors, which enables us to probe this model through the trilepton plus missing-energy search at the LHC. It turns out that the number of events in this channel predicted in our model is in good agreement with that observed by the CMS collaboration. We also discuss prospects for testing this model at the LHC Run-II experiments.