This paper proposes a fountain coding system which has lower decoding erasure rate and lower space complexity of the decoding algorithm than the Raptor coding systems. A main idea of the proposed fountain code is employing shift and exclusive OR to generate the output packets. This technique is known as the zigzag decodable code, which is efficiently decoded by the zigzag decoder. In other words, we propose a fountain code based on the zigzag decodable code in this paper. Moreover, we analyze the overhead, decoding erasure rate, decoding complexity, and asymptotic overhead of the proposed fountain code. As a result, we show that the proposed fountain code outperforms the Raptor codes in terms of the overhead and decoding erasure rate. Simulation results show that the proposed fountain coding system outperforms Raptor coding system in terms of the overhead and the space complexity of decoding.