Twenty-eight structures of the hydrazine trimer have been investigated. Two new types of stable conformations were found. Geometry optimizations were carried out by B3LYP and MP2 methods with the aug-cc-pVDZ basis set. Two stable trimer structures were obtained with one monomer having a saddle-point structure. Three rearrangement reactions were investigated, and several tunneling processes were discussed. The frequency shifts of the antisymmetric wagging and the NH stretching modes were calculated with the MP2/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ methods. With one fitted parameter, the calculated wagging spectrum is in a good accordance with the experimental one.