Mixed-dimension van der Waals (vdW) p-n heterojunction photodiodes have inspired worldwide efforts to combine the excellent properties of 2D materials and traditional semiconductors without consideration of lattice mismatch. However, owing to the scarcity of intrinsic p-type semiconductors and insufficient optical absorption of the few layer 2D materials, a high performance photovoltaic device based on a vdW heterojunction is still lacking. Here, a novel mixed-dimension vdW heterojunction consisting of 1D p-type Se nanotubes and a 2D flexible n-type InSe nanosheet is proposed by a facile method, and the device shows excellent photovoltaic characteristics. Due to the superior properties of the hybrid p-n junction, the mix-dimensional van der Waals heterojunction exhibited high on/off ratios (103) at a relatively weak light intensity of 3 mW cm-2. And a broadband self-powered photodetector ranging from the UV to visible region is achieved. The highest responsivity of the device could reach up to 110 mA W-1 without an external energy supply. This value is comparable to that of the pristine Se device at 5 V and InSe device at 0.1 V, respectively. Furthermore, the response speed is enhanced by one order of magnitude over the single Se or InSe device even at a bias voltage. This work paves a new way for the further development of high performance, low cost, and energy-efficient photodetectors by using mixed-dimensional vdW heterostructures.