The orthogonal properties between different orbital angular momentum (OAM) modes of vortex beams have made it a great potential research area in recent years. Manipulating OAM modes is crucial in most research studies and applications of vortex waves. In this Letter, a manipulating method of OAM mode conversion through a transmission metasurface is proposed. The corresponding OAM mode conversion principles with convolution operation are given. An amplitude and phase controllable metasurface is designed as a device to convert the initial vortex waves carrying single OAM mode or multiple OAM modes to vortex waves with other OAM modes. A metasurface prototype is fabricated and measured to validate the effectiveness of this method. Both simulation and measurement results reflect these functions of converting OAM modes. This work is meaningful not only for the research and development of devices that manipulate OAM modes but also for the transmission, reception, and application of OAM vortex waves in wireless communications and imagining technologies.