It has been long believed that a total mode conversion between longitudinal and shear elastic waves can only be achieved at a certain incidence angle. Here, we show that a total mode conversion can be achieved for a broad range of incidence angles by a specially designed elastic metasurface, namely, transmodal metasurface. From the generalized reflection law, we found that the incident longitudinal wave can be totally converted to a reflected shear wave over a broad range of incidence angles if a sufficiently large phase gradient is introduced at the boundary. Numerical and experimental investigations with a specially engineered transmodal metasurface showed that the total mode conversion can be achieved for wide incidence angles from 19 degrees to 90 degrees, which was impossible to be achieved previously. The proposed idea of the transmodal metasurface can open up an advanced avenue for tailoring elastic wave modes as an outstanding alternative to generating shear waves.