The rare earth iron garnets have been commonly treated like ferromagnets due to the strong exchange coupling between the Fe3+ sublattices. However, the exchange coupling between the rare earth (RE) and transition metal (TM) in the RE-TM compounds is relatively weak and cannot hold the magnetic moments rigidly in a collinear state upon effective anisotropy energy. In this work, we show that a non-collinear magnetic phase is readily presented for a rare earth ferrimagnetic insulator, gadolinium iron garnet (GdIG), when a small magnetic field (H) is applied in the hard axis. We excite magnons from both the collinear and non-collinear magnetic configuration in GdIG via the spin Seebeck effect and detect these magnons in the adjacent normal metal. The comparison between the collinear and non-collinear magnetic configurations reveals a comparable magnon compensating temperature (TMM) for both cases. Moreover, as temperature decreases, the in-plane component of the magnon from the non-collinear case enhances and becomes comparable with that of the collinear case at TMM, representing the dominant role Gd3+ 4f spin plays at low T. Our study shows a wide magnetic tunability in the compensated ferrimagnetic insulator, which offers a myriad of opportunities for magnonic applications.