A lattice Boltzmann scheme for computing on unstructured meshes is proposed. The scheme is based on the finite element method with Galerkin approximation. A program realization of the scheme is implemented with the use of the freefem++ v. 3.20 package. The possibility of the scheme application to practical problems is demonstrated by solving two test problems of computational fluid dynamics. The possibility of the use of equilibrium boundary conditions for the distribution functions is discussed for Reynolds number values less than 100.