We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable $U$ in generalized ensembles to form points on the curve beta(U), the derivative of the logarithmic DOS. Unlike the popular Wang-Landau-like (WLL) methods, FAFE satisfies the detailed-balance condition through out the simulation and automatically generates non-uniform beta points to follow the real change rate of beta(U) in different U regions and in different systems. Combined with a U-compression transformation, FAFE reduces the required simulation steps from O(N(3/2)) in WLL to O(N(1/2)), where N is the system size. We demonstrate the efficiency of FAFE in Lennard-Jones liquids with several N values. More importantly, we show its abilities in finding and identifying different macroscopic states including meta-stable states in phase co-existing regions.