Graphene, as an ideal two-dimensional material, holds great potential for building high-performance sensors. Traditional microfabrication processes, such as lithography and etching, often require multiple complex steps including masking and aligning. Moreover, the graphene is often configured as the semiconducting material in transistors, which add complexity to the system. In this paper, we report the fabrication and characterization of a simple gate-free graphene device. The graphene sheets are made by mechanical exfoliation from bulk graphite and then placed onto a silicon wafer with a thermal oxidization layer. Platinum contact electrodes are fabricated with a mask-free process using focused ion beam, and then expanded by silver paint. An annealing process is used to improve the electrical contact. During the experiment, the fabricated graphene device is used to sense different pH values in the surrounding liquid environment. The results show that the conductance of the graphene increases quadratically with the increasing pH values, which makes the device a high-sensitivity pH sensor. In the end, the possible sensing mechanisms of our graphene device are discussed.