We introduced a generalized lattice-spring lattice-Boltzmann model (GLLM) for numerical simulation of flexible bodies in fluids. Validation of GLLM is conducted by comparing our results with existing theoretical and experimental results. Swimming of a flexible filament driven by its header with a harmonic function is simulated at Reynolds numbers ranged 0.15-5.1. The wave patterns of the filament are consistent with the theory of elastohydrodynamics at low Reynolds number and the wave wriggles increase as the Reynolds number increases. Intensity of vortices and propulsive force increases as Reynolds number increases. a r t i c l e i n f o

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