Laser welding plant for laser welding TWIP steel tubular components; the laser welding plant comprises two mandrels, which are coaxial and opposing along an alignment axis and are mounted for relatively moving and assuming: - respective locking positions, where the mandrels are spaced apart for receiving and locking axially, in a position coaxial to the alignment axis, respective first and second tubular pieces, - and respective welding positions, where the mandrels are arranged closely so as for bringing in contact end sections of the respective first and second tubular pieces to be welded; characterized in that the laser welding plant further comprises: - a laser welding head including a fibre laser operable to weld the end sections of the tubular pieces when the mandrels are in the respective welding positions, - a position sensor configured to measure an axial position of one of the tubular pieces in one of the mandrels when the mandrel is in the locking position, - and an electronic control unit connected to the mandrels, to the laser welding head and to the position sensor and configured to cause the mandrels to move into the respective welding positions taking into account any deviation previously measured by the position sensor, and to maintain the tubular pieces axially pressed together during welding; wherein the electronic control unit is further configured to cause the laser welding head to perform a welding cycle comprising: - an initial pre-welding step where pre-welding spots obtained with a laser pulse power from 250 to 800 W and for a laser pulse width from 100 to 600 ms are applied, - a ramp-up welding step having a duration ranging from 150 to 600 ms and a welding power increasing from 250 to 800 W; - a welding step having a duration from 2500 to 4500 ms and a constant laser power from 1200 to 2500 W, and - a ramp-down welding step having a duration from 150 to 600 ms and a welding power decreasing from 800 to 250 W. - respective locking positions, where the mandrels are spaced apart for receiving and locking axially, in a position coaxial to the alignment axis, respective first and second tubular pieces, - and respective welding positions, where the mandrels are arranged closely so as for bringing in contact end sections of the respective first and second tubular pieces to be welded; - a laser welding head including a fibre laser operable to weld the end sections of the tubular pieces when the mandrels are in the respective welding positions, - a position sensor configured to measure an axial position of one of the tubular pieces in one of the mandrels when the mandrel is in the locking position, - and an electronic control unit connected to the mandrels, to the laser welding head and to the position sensor and configured to cause the mandrels to move into the respective welding positions taking into account any deviation previously measured by the position sensor, and to maintain the tubular pieces axially pressed together during welding; wherein the electronic control unit is further configured to cause the laser welding head to perform a welding cycle comprising: - an initial pre-welding step where pre-welding spots obtained with a laser pulse power from 250 to 800 W and for a laser pulse width from 100 to 600 ms are applied, - a ramp-up welding step having a duration ranging from 150 to 600 ms and a welding power increasing from 250 to 800 W; - a welding step having a duration from 2500 to 4500 ms and a constant laser power from 1200 to 2500 W, and - a ramp-down welding step having a duration from 150 to 600 ms and a welding power decreasing from 800 to 250 W.