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