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In this paper, the parallel-distributed block-latency insertion method (block-LIM) is proposed for the fast transient analysis of a large-scale circuit that includes lots of coupling elements, such as mutual inductance and mutual capacitance. A conventional SPICE-like simulator requires an enormous cost for transient analysis of large-scale equivalent network that includes tightly coupled transmission lines, which is derived by using well-established commercially based extractors. The proposed method is based on the leapfrog algorithm, and can efficiently analyze tightly coupled transmission lines. First, the original LIM and the block-LIM are reviewed briefly. Next, the parallel-distributed block-LIM is proposed for the fast transient simulation and is implemented on the personal-computer-cluster system. Finally, some numerical results are shown, and it is confirmed that the proposed technique is useful and efficient for the simulations of the tightly coupled transmission lines.