Logic computation | Framework nucleic acid | mRNA imaging | DNA circuits | Four-way strand exchange DNA circuits have been designed for implementation of various functions based on DNA strand displacement in cell-free settings, but their capabilities in biological environments remain limited. In this work, we report framework nucleic acid (FNA)-based circuits enabling intracellular logic computation for mRNA imaging. FNAs as rigid scaffolds enable to deliver our built DNA circuits into cells without aid of transfection reagents, evading a time-consuming and tedious process prior to analysis, and the pendant duplex DNA designed at one vertex of FNA as gate is suitable for four-way strand exchange, minimizing crosstalk with other nucleic acids in the cellular milieu. We demonstrated that such FNA-based circuits can operate both in vitro and in vivo logic computation, including OR and AND logic gates. Moreover, in situ mRNA imaging was also realized by exploiting native mRNA as scaffolds to bind multiple FNA-based gates for the enhanced signal-to-background ratio. We hope that this FNA-based circuit can be applied for disease diagnosis, facilitating the development of biomedicine.