Gyroscopic effects may change the stability, dynamic behaviour and vibratory responses of the systems at high-speed applications in a significant manner. In this study, a new linear time-invariant lumped mass model in three-dimensional space is developed with a high emphasis on gyroscopic effects for a double-helical planetary gear system. In the developed model, each member has six degrees of freedom where both the mesh and the bearing stiffness are considered. The forced responses, due to gear mesh transmission error excitations, are calculated through the modal summation technique. The natural modes are extracted from the corresponding eigenvalue problem for the undamped system. The obtained results indicate the reduction in most of the natural frequencies by applying the gyroscopic effects in double-helical planetary gear systems. By considering the gyroscopic effects in this newly proposed model, the root mean square (RMS) amplitudes of vibration are changed in different directions. To verify this developed model and solution method, the obtained natural frequencies and forced responses are compared with those obtained in other studies.