This study develops and demonstrates a sensor based on a strongly coupled seven-core fiber (SCF) supermode Bragg grating for multiparameter measurements. Two Bragg resonance notches are observed in the transmission spectrum, corresponding to HE₁₁-like and HE₁₂-like supermodes of the SCF. Because the SCF is spliced between two standard single-mode fibers with central alignments at both ends, the transmission spectrum of the device also comprises an interferometric profile owing to the Mach-Zehnder interference of the supermodes. The responses of the device to temperature and strain are experimentally characterized. The obtained temperature and strain sensitivities of the supermode Bragg grating notches are 9.56 pm/℃, 9.55 pm/℃ and 0.64 pm/με, 0.584 pm/με, respectively. The obtained temperature and strain sensitivities of interferometric dips are 11.8 pm/℃ and -0.925 pm/με, respectively. This device can be potentially used to measure the temperature and strain simultaneously.