A new lattice Boltzmann method to simulate open channel flows with complex geometry described by a conservative form of Saint-Venant equations (LBCSVE) is developed. The Saint–Venant equations include an original treatment of the momentum equation source term. Concrete hydrostatic pressure thrust expressions are provided for rectangular, trapezoidal and irregular cross-section shapes. A D1Q3 lattice arrangement is adopted. External forces, such as bed friction and the static term, are discretised with a centred scheme. Bounce back and imposed boundary conditions are considered. To verify the LBCSVE model, four cases are carried out: tidal flow over a regular bed in a rectangular cross section, steady flow in a channel with horizontal and vertical contractions, steady flow over a bump in a trapezoidal channel and steady flow in a non-prismatic channel with friction. Results indicate that the proposed scheme is simple and can provide accurate predictions for open channel flows.