This present paper proposes aerodynamic forces and entropy generation characteristics on the flow past two-dimensional airfoil at low Reynolds number by multiple-relaxation-time lattice Boltzmann method to clarify the flow loss mechanism. The block mesh refinement was adopted in which a higher accuracy was needed in parts of the domain characterized by complex flow. The interpolated bounce-back method was used to treat the irregular curve. This numerical method can effectively solve the complex flow field simulation problems with reasonable accuracy and reliability by simulating flow around plate and airfoil. Based on second law of thermodynamics, an expression of entropy generation rate for arbitrary control volume was derived theoretically which could accurately quantify the local irreversible loss of the flow field at any position. After that, a comprehensive numerical study was conducted to analyze relationship of entropy generation and drag force by taking NACA0012 airfoil as the research object. For unsteady condition, entropy generation rate and the drag force are not linearly related any more. Losses due to steady effects mainly consider the irreversibility in the boundary layer and wake while the unsteady effects come from the interaction between the main separation vortex and the trailing shedding vortex.