Low-density parity-check (LDPC) codes become very popular in channel coding, since they can achieve the performance close to maximum-likelihood (ML) decoding with linear complexity of the block length. Recently, Muramatsu et al. proposed a code using LDPC matrices for Slepian-Wolf source coding, and showed that their code can achieve any point in the achievable rate region of Slepian-Wolf source coding. However, since they employed ML decoding, their decoder needs to know the probability distribution of the source. Hence, it is an open problem whether there exists a universal code using LDPC matrices, where universal code means that the error probability of the code vanishes as the block length tends to infinity for all sources whose achievable rate region contains the rate pair of encoders. In this paper, we show the existence of a universal Slepian-Wolf source code using LDPC matrices for stationary memoryless sources.