MT19937 is a kind of Mersenne Twister, which is a pseudo-random number generator. This study presents new designs for a MT19937 circuit suitable for custom computing machinery for high-performance scientific simulations. Our designs can generate multiple random numbers per cycle (multi-port design). The estimated throughput of a 52-port design was 262 Gbps, which is 115 times higher than the software on a Pentium 4 (2.53 GHz) processor. Multi-port designs were proven to be more cost-effective than using multiple single-port designs. The initialization circuit can be included without performance loss in exchange for a slight increase of logic scale.