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This article describes simulation study on SQUID applications for Single-Flux-Quantum(SFQ) Logic Circuits. Here, a SQUID is compatible to a Quantum Flux Parametorn (QFP). Several new circuits based on a SQUID are investigated. A cascaded SQUID is proposed with the signal amplitude in the same order of an SFQ. An SFQ-pulse driving circuits with the new SQUID are successfully simulated. An SFQ trap which catches SFQs is newly proposed. Focusing on a circulating current of a segment in a Josephson transmission line (JTL), an SFQ-pulse is non-destructively detected by a SQUID. A conventional SQUID inserted in a JTL operates as a gate which controls SFQ-pulse transmission through it. Compatibility of SQUIDs and SFQ circuits is demonstrated.