Highly sensitive broadband photodetection is of critical importance for many applications. However, it is a great challenge to realize broadband photodetection by using a single device. Here we report photodetectors (PDs) based on three-dimensional (3D) graphene foam (GF) photodiodes with asymmetric electrodes, which show an ultra-broadband photoresponse from ultraviolet to microwave for wavelengths ranging from ${10}^2$ to ${10}^6\mathrm{nm}$. Moreover, the devices exhibit a high photoresponsivity of ${10}^3\mathrm{A}·{\mathrm{W}}^{?1}$, short response time of 43 ms, and 3 dB bandwidth of 80 Hz. The high performance of the devices can be attributed to the photothermoelectric (PTE, also known as the Seebeck) effect in 3D GF photodiodes. The excellent optical, thermal, and electrical properties of 3D GFs offer a superior basis for the fabrication of PTE-based PDs. This work paves the way to realize ultra-broadband and high-sensitivity PDs operated at room temperature.