Although graphene has the longest mean free path of carriers of any known electronic material, very few novel devices have been reported to harness this extraordinary property. Here we demonstrate a ballistic nano-rectifier fabricated by creating an asymmetric cross-junction in single-layer graphene sandwiched between boron nitride flakes. A mobility ~200,000 cm2 V−1 s−1 is achieved at room temperature, well beyond that required for ballistic transport. This enables a voltage responsivity as high as 23,000 mV mW−1 with a low-frequency input signal. Taking advantage of the output channels being orthogonal to the input terminals, the noise is found to be not strongly influenced by the input. Hence, the corresponding noise-equivalent power is as low as 0.64 pW Hz−1/2. Such performance is even comparable to superconducting bolometers, which however need to operate at cryogenic temperatures. Furthermore, output oscillations are observed at low temperatures, the period of which agrees with the lateral size quantization.