A multi-stage transmission for a vehicle includes an input shaft, an output shaft, first to fourth planetary gear devices each having three rotary elements and transmitting rotary forces between the input and output shafts, and at least six shifting elements connected to the rotary elements of the planetary gear devices. Of the first planetary gear device, the first rotary element is installed to be fixable by any one of the shifting elements and permanently connected to the second rotary element of the third planetary gear device and the third rotary element of the fourth planetary gear device, the second rotary element is variably connected to the third rotary element of the second planetary gear device and the third rotary element of the third planetary gear device, and the third rotary element is variably connected to the first and second rotary elements of the second planetary gear device.