Submillimetre images of transition discs are expected to reflect the distribution of the optically thin dust. Former observation of three transition discs LkHα 330, SR 21N and HD 1353444B at submillimetre wavelengths revealed images which cannot be modelled by a simple axisymmetric disc. We show that a large-scale anticyclonic vortex that develops where the viscosity has a large gradient (e.g. at the edge of the disc dead zone), might be accountable for these large-scale asymmetries. We modelled the long-term evolution of vortices being triggered by the Rossby wave instability. We found that a horseshoe-shaped (azimuthal wavenumber m = 1) large-scale vortex forms by coalescing of smaller vortices within 5 × 104 yr, and can survive on the disc lifetime (∼5 × 106 yr), depending on the magnitude of global viscosity and the thickness of the viscosity gradient. The two-dimensional grid-based global disc simulations with local isothermal approximation and compressible-gas model have been done by the GPU version of hydrodynamic code fargo (gfargo). To calculate the dust continuum image at submillimetre wavelengths, we combined our hydrodynamical results with a three-dimensional radiative transfer code. By the striking similarities of the calculated and observed submillimetre images, we suggest that the three transition discs can be modelled by a disc possessing a large-scale vortex formed near the disc dead zone edge. Since the larger dust grains (larger than mm in size) are collected in these vortices, the non-axisymmetric submillimetre images of the above transition discs might be interpreted as active planet and planetesimal-forming regions situated far (≳50 au) from the central stars.