In the process of deep-sea mining, the liquid-solid flows in the vertical transportation pipeline are very complex. In the present work, an in-house solver MPSDEM-SJTU based on the improved MPS and DEM is developed for the simulation of hydraulic conveying. Firstly, three examples including the multilayer cylinder collapse, the Poiseuille flow and two-phase dam-break are used to validate the precision of the DEM model, the pipe flow model and MPS-DEM coupling model, respectively. Then, the hydraulic conveying with coarse particles in a vertical pipe is simulated. The solid particle distribution is presented and investigated in detail. Finally, the coupling method is successfully applied for the simulation of the liquid-solid flows in a vertical pipe with rotating blades, which shows the stability of the solver under rotating boundary conditions. This fully Lagrangian model is expected to be a new approach for analyzing hydraulic conveying.