A novel system decoupling approach (SDA) that enables three degree-of-freedom (3-DOF) bridge flutter analysis is proposed in this study to simultaneously investigate the relationships between modal parameters and 18 flutter derivatives. Based on the incentive-feedback mechanisms, the aerodynamic coupled system is conveniently decoupled in an iterative solution. Based on the SDA, it is unnecessary to simultaneously calculate all multiple frequencies for determining modal parameters and eventually quantifying critical flutter wind velocity. The efficacy and accuracy of the SDA is verified using a numerical example of thin flat plate. The coupling effects among three DOFs and influence of 18 flutter derivatives on flutter performance are quantified using the newly proposed method. The flutter mechanisms of thin flat plate and bluff deck section of the Akashi Kaikyo Suspension Bridge are numerically examined, and both difference and common grounds for two typical flutter phenomena are summarized. The results by the SDA show good agreement with those by the commonly used complex eigen-value analysis (CEVA). For the Akashi Kaikyo Bridge with bluff deck section, the analytical results of 2-DOF coupled flutter are coincident with the 3-DOF case and the experimental observations. This study provides significant insights into the flutter characteristics of 3-DOF bridges and explores the roles played by various parameters in modifying bridge deck aerodynamics and the evolution of modal coupling with increasing wind velocity. The simplified formulation that only concerns is presented, by which acceptable accuracy of flutter parameters can also be achieved for torsional modal branch. It is validated using a thin flat plate and the Akashi Kaikyo Bridge with bluff deck.