The lattice Boltzmann method (LBM) coupled with large eddy simulation (LES) has become an established approach for turbulent flow simulations. This method usually needs refined mesh grids and costs high computational expenses, thus constructing the reduced order model (ROM) for acceleration is important. In the present paper, a novel ROM for LBM is proposed. Compared with existing ROM for LBM, the proposed model is successfully extended to couple with LES by the following two works: resolving the nonlinearity in the equilibrium distribution function by introducing \(L^2\) space theory; developing a perturbation based LES model (PLES) to mitigate the nonlinearity caused by the eddy viscosity. Three benchmark numerical experiments demonstrate that the proposed model is convergent, accurate, and achieves a substantial acceleration compared with conventional approaches.