A latch assembly having adjusting backset includes a casing, a latch bolt and a latch rear section. The latch bolt includes a bolt body and a fixed member connected with the bolt body. The top of the fixed member includes two positioning notches adapted to different backsets. A positioning member and the fixed member are disposed in a slide. The positioning member includes a positioning projection corresponding to the positioning notch at the front portion thereof. The latch includes a pin that can lift the positioning member to disengage the positioning projection from the positioning notch. Then, the positioning projection is moved to another positioning notch, thereby changing the backset. The latch assembly includes a positioning spring to keep the positioning projection fixed in the positioning notch. The latch assembly may include an upper connecting member, a lower connecting member and an assembly member to strengthen the latch assembly.