With an effective Lagrangian approach, we give a full analysis on the (N) over barN -> (N) over barN pi pi and reactions by exploring the roles of various resonances with mass up to 1.72 GeV. We find large contributions from Delta, N*(1440), Delta(1600) and Delta(1620) resonances. Our calculations also indicate sizeable contributions from nucleon poles for the energies close to the threshold. A good description to the existing data of different isospin channels of NN -> NN pi pi and (N) over barN -> (N) over barN pi pi for beam energies up to 2.2 GeV is reached. Our results provide important implications to the ABC effect and guildlines to the future experimental projects at COSY, HADES and HIRFL-CSR. We point out that the at FAIR could be an essential place for studying the properties of baryon resonances and the data with baryon and anti-baryon in final states are worth analyzing.