Low threshold and widely tunable InAs/GaAs quantum-dot lasers are implemented with grating-coupled external-cavity arrangement. Throughout the tuning range of 130 nm, from 1160 to 1290 nm, the threshold current density is not more than 0.9 kA/cm2 and no noticeable threshold jump is observed. For a shorter-cavity device, the injection current is kept at a record low value of 90 mA but the tuning range is further extended to 150 nm, from 1143 to 1293 nm. The effect of cavity length on the tuning characteristics is discussed and the strategy for design and optimization of multilayer quantum-dot structure is also proposed.