Conical beams have recently attracted much attention due to their excellent performances and potential applications in wireless and satellite-based communication technology. Here, reflective metasurfaces composed of Pancharatnam-Berry (PB) phase elements are demonstrated to have the ability to be flexible and to fully control the conical beam generation with desirable orbital angular momentum (OAM) modes. The theoretical model is developed to analyze the behavior of the conical beam radiation from the reflective metasurface and especially to predict the cone angle, one of the most important factors in the conical beam design. Analysis shows that arbitrary combinations of the cone angle and the OAM mode can be obtained by synthesizing the spatial phase distribution of the metasurface. Finally, two prototypes of microwave metasurfaces, with working bands from 14 GHz to 17 GHz, are fabricated and measured, and the results agree well with the theoretical predictions and simulations. This work demonstrates that metasurfaces can be used for controlling the conical beam generation with desirable OAM modes to potentially enable high capacity data communication, paving the way for novel devices with an appealing low-profile in wireless communication applications.