A miniature fiber-tip pressure sensor was built by using an extremely thin graphene film as the diaphragm. The graphene also acts as a light reflector, which, in conjunction with the reflection at the fiber end-air interface, forms a low finesse Fabry-Perot interferometer. The graphene based sensor demonstrated pressure sensitivity over 39.4 nm/kPa with a diaphragm diameter of 25 μm. The use of graphene as diaphragm material would allow highly sensitive and compact fiber-tip sensors.