We obtain global solutions for radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self‐consistently determined by mixing‐length theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solutions correspond to large viscosity parameter α≳ 0.1– they are purely advection‐dominated with no convection; they have been extensively studied in the literature. Type II solutions are for moderate α∼ 0.01, and have a three‐zone structure. The inner zone is advection‐dominated, the middle zone is convection‐dominated and ranges from a few tens to a few thousands of gravitational radii, and the outer zone is convectively stable and outwardly matches a Keplerian disc. The net energy flux throughout the flow is inward, as in type I solutions. Type III solutions, which are for small α≲ 0.001, consist of two zones as Abramowicz et al. suggested previously: an inner advection‐dominated zone and an outer convection‐dominated zone, separated at a radius of a few tens of gravitational radii. This type of solution has an outward net energy flux. In both type II and type III solutions, the radial density profile is between the 1/2 law of the self‐similar convection‐dominated accretion flow model and the 3/2 law of the self‐similar advection‐dominated accretion flow model, and the efficiency of energy release is found to be extremely low. Our results are in good agreement with those of recent numerical simulations.