To solve the problem of high error floor for LT codes in additive white gaussian noise (AWGN) channels, an improved coding scheme is designed in this paper. The main idea is to design an expanding window to mark the low-degree information nodes, and these nodes will be selected by the check node preferentially. Besides, the average degree of check nodes is increased to improve the elimination efficiency of low-degree information nodes. The bit error rate (BER) performance and iterative convergence of the proposed scheme are analyzed, and the optimal parameters for different coding conditions are designed. Simulation results show that compared with the conventional LT code, the error floor can be reduced by nearly 5 orders of magnitude for the proposed scheme. Besides, the designed LT code outperforms the existing LT codes in literature in terms of BER performance.