A concatenated scheme combining short length Luby Transform(LT) codes with traditional error correcting codes is proposed for the requirement of short erasure correcting codes in real-time communication. Considering the complexity and overhead of the scheme, Reed Solomon-Convolution coding(RS-CC) is used for the construction of equivalent erasure channels, and the short LT codes are concatenated for the correction of erasure errors. A decoding algorithm is proposed for the short LT codes, and the degree distribution selection method is shown for small message length. Simulation results demonstrate that, comparing with the existing codes, less overhead is needed and the reliability of the concatenated scheme is enhanced.