A latch bolt mechanism of a tubular lock allows adjustment in backset by using an extension casing. The latch bolt mechanism has a latch bolt housing having a latch bolt mounted therein, the latch bolt being movable beyond a face plate or retracted into the face plate. Two plates are connected together and mounted to an inner end of the latch bolt. The plates includes aligned two first positioning holes, aligned second positioning hole, and aligned openings. An actuating plate is mounted between the plates and includes an end operably connected to the latch bolt. The other end of the actuating plate includes two teeth each having a block formed thereon. The blocks are pressed against by a follower plate that also includes two teeth. When either tooth of the actuating plate or the follower plate is pressed against by a spindle of the lockset, the latch bolt is retracted. An extension casing is mounted around the plates and movable toward or away from the latch bolt housing. The extension casing includes a first hole and a second hole through which the spindle of the lockset is selectively extended.