A novel hybrid interferometer sensor composed of a tapered seven-core fiber (TSCF) and a polydimethylsiloxane (PDMS) cap at the end face of a TSCF is proposed for simultaneous measurement of temperature and gas pressure. TSCF forms a Michelson interferometer (MI), and the PDMS cap on the end surface of TSCF forms a Fabry-Perot interferometer (FPI). The sensing head consisted of a cascade of MI and FPI. When the external temperature or gas pressure changes, owing to the thermal effect or elastic deformation of PDMS, the interference spectrum of the FPI shifts significantly, so the FPI is very sensitive to temperature and gas pressure. MI, which is made of quartz optical fibers, is sensitive only to temperature and is not sensitive to gas pressure. The experimental results show that FPI has a temperature sensitivity of -0.22 nm/°C in the temperature range of 40 °C to 80 °C, and a gas pressure sensitivity of -2.27 nm/MPa in the gas pressure range of 0 to 0.3 MPa. MI has a temperature sensitivity of 0.05 nm/°C in the temperature range of 40 °C to 80 °C, and a gas pressure sensitivity of zero in the gas pressure range of 0 to 0.3 MPa. Using the temperature and gas pressure sensitivities of FPI and MI to construct a measurement matrix, it is possible to simultaneously measure temperature and gas pressure, eliminating their cross-sensitivity. This sensor has the comprehensive advantages of compact structure, small size, easy manufacturing, low cost, high reliability, and high sensitivity, and is expected to be applied in industrial practice.