We report a graphene-based frequency-selective terahertz (THz) and infrared (IR) detector. The experimental results have demonstrated that the graphene transistor under a magnetic field is capable of detecting THz and IR waves in a very wide band of frequencies (0.76-33 THz) and that the detection frequency is tuned by changing the magnetic field. We have further imaged electric potential distribution in the graphene detector and have observed local step structure associated with impurities. The THz and IR photoconductivity properties of graphene are likely to be sensitive to such potential steps.