An all annealing-free solution-manufacturing is regarded as a technological advancement for the development of flexible organic solar cells (OSCs), which can prevent the distortion of plastic substrates, avoid destroying the active components of the devices, and simplify the device fabrication. Here, we report an efficient all annealing-free solution-processed flexible OSC integrated on a soft polyethylene (PE) substrate. The transparent anodes, hole-transport layers, active layers and electron-transport layers are solution-processed at room temperature without thermal annealing treatments. Thanks to both the as-developed gentle superacid doping and air-drying treatments at room temperature that enable a high-merit flexible anode on the soft PE substrates, the annealing-free flexible OSCs yield a high efficiency of 14.66% along with a high power-per-weight of 6.33 W g, which is close to that (15.73%) of thermally annealed rigid OSCs based on indium tin oxide anodes. Due to the mild annealing-free solution-processing and the soft PE substrates having an extremely low Young's modulus of only 0.2 GPa, the flexible OSCs maintain a high flexibility in a harsh bending test.