A novel Mach-Zehnder interferometer pressure sensor was proposed by cascading single mode fiber with multimode fiber. It was fabricated by just splicing a single mode fiber with two short section of multimode fibers. The core-cladding modes interference of the single mode fiber was obtained due to the core mismatch, which made the change of outside pressure more directly acted on the light field inside of the single mode fiber, so a high pressure sensitivity can be achieved. In order to obtain a well-defined interference pattern, the length of the sensor was defined as 39 mm after many experiments. The experimental results show that with the increasing of the pressure, the transmission spectrum of the sensor appears red shift phenomenon obviously, the pressure sensitivity of the sensor is 554.830 pm/N and the linearity is 0.984 in the range of 2~16N pressure changes. The sensor has advantages such as simple structure, easy manufacturing, low cost, high sensitivity and so on, it can be well applied to pressure sensing field.