Polarisation-state conversion from parallel linear polarisation to orthogonal linear polarisation was successfully demonstrated using a birefringence crystal for the two longitudinal oscillation modes of a dual-mode Nd:YVO 4 microchip laser. The laser emitted two longitudinal oscillation modes simultaneously in the vertical linear polarisation state with a frequency difference of 101 GHz. In the experiment, it was shown that by using a 17-mm-long LiNbO 3 birefringence crystal, it was possible to almost perfectly convert the polarisation state of the two oscillation modes by providing a π-rad difference in phase retardations between the two oscillation modes. The residual elliptic component was eliminated using a pair of waveplates.