In previous works, density evolution schemes have been used to design an irregular low-density paritycheck (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.